High-precision mems flexible array displacement meter and measuring method for internal displacement monitoring of earth-rockfill dam

Abstract

The application discloses a high-precision MEMS flexible array displacement meter for internal displacement monitoring of earth-rock dams and a measuring method, and relates to the internal displacement monitoring technology of earth-rock dams.The method is characterized in that the MEMS array displacement meter composed of rigid measuring units and flexible connecting units is lowered into a hole through drilling construction, and the hole is filled with graded fine sand in layers and vibrated to ensure rigid connection with the dam body;acceleration data are collected by using a triaxial MEMS acceleration sensor, and after removing abnormal values by a variation coefficient method and performing exponential weighted moving average filtering, the inclination angle is calculated based on gravity components;the relative displacement is derived in combination with the fixed interval of adjacent units and the geometric projection relationship, and the cumulative displacement at different depths is accumulated to form a complete monitoring profile;the drilling depth is accurately calculated according to dam body parameters, the collection frequency is dynamically adjusted according to the deformation rate, the dam body flexible deformation is adapted, and full-depth high-precision monitoring is realized to provide reliable data support for dam safety evaluation.

Description

Technical Field

[0001] This invention relates to the field of displacement monitoring technology for earth-rock dams, specifically to a high-precision MEMS flexible array displacement meter and measurement method for displacement monitoring inside earth-rock dams. Background Technology

[0002] Earth-rock dams, as key water-retaining structures in hydraulic engineering, are directly related to the safety and property of people downstream and to socio-economic development. During long-term operation, factors such as the weight of the dam materials, water pressure, seepage deformation, and changes in geological conditions can easily lead to uneven settlement, sliding, or shear deformation within the dam body. If these are not monitored and preventative measures are not taken in a timely manner, they may cause major accidents such as dam cracks, leakage, or even dam failure. Therefore, high-precision, real-time monitoring of displacement at different depths within the earth-rock dam is a core means of assessing the structural safety of the dam and providing early warning of potential risks.

[0003] Traditional dam displacement monitoring relies heavily on external deformation observations (such as leveling and GNSS surface monitoring), which only reflect surface deformation and cannot capture displacement characteristics of deep internal structures, making it difficult to provide early warning of hidden damage within the dam. While existing deep displacement monitoring technologies, such as the combination of inclinometer tubes and inclinometers, can achieve monitoring at a certain depth, they suffer from problems such as high equipment rigidity, poor coordination with dam deformation, and measurement accuracy being greatly affected by installation techniques. Fiber optic sensing technology, while offering advantages in distributed monitoring, is susceptible to temperature interference, has low survival rates in complex dam environments, and is costly. Therefore, there is an urgent need for a technical solution that can adapt to the flexible deformation of the dam body, achieve high-precision monitoring at all internal depths, and is easy to install and highly stable, in order to overcome the shortcomings of existing technologies.

[0004] In the field of earth-rock dam displacement monitoring, traditional technical solutions are mainly divided into two categories: surface monitoring and deep-body monitoring. Surface monitoring technologies are represented by leveling, total station measurement, and GNSS positioning: Leveling reflects settlement by measuring the elevation changes of key points such as the dam crest and slope, with an accuracy of millimeters, but it relies on manual operation, has a long monitoring cycle, is difficult to achieve real-time dynamic monitoring, and is significantly affected by terrain and weather; GNSS technology can achieve automated surface displacement monitoring, but its signal is easily blocked by vegetation and buildings on the dam body, and the multipath effect leads to a decrease in accuracy, and it cannot obtain deformation data inside the dam body.

[0005] Traditional methods for deep displacement monitoring primarily rely on inclinometer tubes combined with mechanical inclinometers. This involves embedding inclinometer tubes in boreholes within the dam body, then using an inclinometer to slide along a guide groove inside the tube to measure the tilt angle at different depths, thereby calculating the displacement. While this technology is simple in principle and low in cost, it has significant drawbacks: First, the inclinometer tube is a rigid structure, resulting in poor coordination with dam deformation and a high risk of breakage due to uneven dam settlement, leading to monitoring interruptions. Second, mechanical inclinometers require manual point-by-point measurements, which is inefficient, and the accuracy is greatly affected by the operator's skill. Third, the filling material between the inclinometer tube and the dam body is prone to loosening, causing the monitoring data to fail to accurately reflect dam deformation. Furthermore, some projects use layered settlement meters to monitor vertical displacement, but these cannot obtain horizontal displacement data, making it difficult to comprehensively assess the three-dimensional deformation state within the dam body.

[0006] With the development of sensing technology, deep displacement monitoring technology based on MEMS (Micro-Electro-Mechanical Systems) is gradually being applied in engineering practice. In existing technologies, some solutions use array sensors composed of MEMS accelerometers or gyroscopes to calculate displacement by measuring tilt angles. However, their structural design and data processing methods still have shortcomings: for example, some devices use rigid rods connected in series with sensors, which, while ensuring the stability of the measurement unit, cannot adapt to the flexible deformation of the dam body and are prone to structural damage in areas of large deformation; some solutions do not optimize the data acquisition frequency for the special environment of the dam body, leading to data loss or redundancy when the deformation rate changes abruptly, affecting monitoring accuracy.

[0007] Chinese patent CN115855032A discloses an "integrated displacement monitoring device and method that combines GNSS and MEMS deep displacement technologies". Its core is to connect a MEMS triaxial accelerometer with a rigid rod to form a single-section array sensor, which is then connected in series with a GNSS pole to realize surface and deep displacement monitoring through angle calculation. While this technology achieves a combination of surface and deep monitoring, it suffers from several serious drawbacks: First, the use of rigid rods to connect sensors cannot adapt to the complex flexible deformations within earth-rock dams. When the dam undergoes significant bending or shear deformation, the rigid structure is prone to stress concentration, leading to damage and loss of monitoring capability. Second, no effective solution has been proposed for handling the gap between the borehole and the sensor. Relying solely on the equipment's own weight to bury it in the soil makes it difficult to ensure a rigid connection between the sensor and the dam, making the monitoring data susceptible to environmental interference. Third, the data processing does not consider the impact of dam material properties (such as internal friction angle and compression modulus) on the monitoring depth, limiting its applicability to general soil types and failing to meet the full-depth monitoring requirements of earth-rock dams. Fourth, it relies on GNSS to correct surface displacement, but earth-rock dams often have wave walls, gate hoists, and other facilities on their crests, making GNSS signals easily blocked, leading to correction failure and affecting overall monitoring accuracy. Summary of the Invention

[0008] Based on the aforementioned technical problems, this application discloses a high-precision MEMS flexible array displacement gauge and measurement method for monitoring displacement inside earth-rock dams. The measurement method specifically includes:

[0009] S1. Drilling is carried out in the pre-set monitoring area of ​​the earth-rock dam; the diameter of the borehole is adapted to the outer diameter of the MEMS flexible array displacement meter, and the borehole axis is kept perpendicular.

[0010] S2. Slowly lower the MEMS flexible array displacement gauge along the borehole so that the rigid measuring units of the MEMS flexible array displacement gauge are evenly distributed at different depths in the borehole. Fill the gap between the borehole and the displacement gauge with graded fine sand and compact it to ensure that the displacement gauge forms a rigid connection with the dam structure and moves synchronously with the deformation of the dam.

[0011] S3. After the fine sand filling stabilizes, the acceleration signal at the location is collected by the triaxial MEMS accelerometer of the rigid measurement unit of the MEMS flexible array displacement meter, and the acceleration data at different times is recorded.

[0012] S4. Preprocess the collected acceleration data, remove outliers and perform smoothing filtering, and calculate the tilt angle of each rigid measurement unit in the monitoring plane based on the gravitational acceleration components.

[0013] S5. Based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle, calculate the relative displacement between the rigid measuring units through geometric projection relationship;

[0014] S6. Accumulate the relative displacement of each segment along the direction of displacement gauge installation to obtain the cumulative displacement value at different depths inside the dam body, forming a complete displacement monitoring profile.

[0015] Preferably, the drilling depth in S1 is determined based on the dam monitoring requirements. This is achieved through a full-depth monitoring scenario from the dam crest to the dam foundation. The maximum dam height needs to be covered. Depth of influence of shallow foundation The shallow depth of influence of the dam foundation Based on the internal friction angle of the dam material The difference in water head between the upstream and downstream sides of the dam body and the compression modulus of the dam foundation soil Confirmed, the formula is: ,in .

[0016] Preferably, in step S2, graded fine sand is filled into the gap between the borehole and the displacement gauge and then compacted by vibration. A layered filling method is adopted. First, graded fine sand with a preset thickness is filled into the gap. Then, a vibrating rod with a diameter adapted to the gap width is inserted into the fine sand. The vibrating rod is moved evenly along the circumference of the borehole and vibrated until there is no obvious sinking on the surface of the fine sand. Then, the next layer of graded fine sand is filled. The above filling and vibration are repeated until the gap between the borehole and the displacement gauge is completely filled with graded fine sand.

[0017] Preferably, the triaxial MEMS accelerometers of each rigid measurement unit in S3 are arranged along the three orthogonal directions X, Y, and Z, and the data acquisition frequency of the triaxial MEMS accelerometers is... Based on the dam deformation rate Confirmed, the formula is: ,in This is the proportionality coefficient. This represents the real-time deformation rate of the dam monitoring area. This indicates rounding up, and the sampling frequency increases with the deformation rate.

[0018] Preferably, in step S4, the collected acceleration data is preprocessed to remove outliers and perform smoothing filtering. Specifically, outliers are identified using the coefficient of variation method, and the coefficient of variation of the acceleration data sequence continuously collected from the same rigid measurement unit is calculated. The formula is: ,in The mean of the sequence. The standard deviation of a sequence is defined as the absolute value of the deviation of a data point from the mean. It was determined to be an outlier at that time. To predetermine the multiplier, outliers are replaced with the weighted average of three consecutive valid data points. The weights increase linearly with increasing distance. An exponentially weighted moving average is used for smoothing filtering, and the filtering formula is as follows: ,in This is the original data at the current moment. This is the filtering result at the current moment. This is the filtering result from the previous moment. The smoothing coefficient is used to process the acceleration data sequence point by point to obtain a smoothed signal.

[0019] Preferably, in step S4, the tilt angle of each rigid measuring unit in the monitoring plane is calculated based on the gravitational acceleration components. Specifically, the preprocessed acceleration data is analyzed, and the triaxial gravitational acceleration components of each rigid measuring unit in a static state are extracted. The X-axis and Y-axis components reflect the horizontal projection of gravity, and the Z-axis component reflects the vertical projection of gravity. The tilt angle in the X-direction is calculated by the ratio of the X-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: The tilt angle in the Y direction is calculated by the ratio of the Y-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: ,in The tilt angle is in the X direction. The tilt angle in the Y direction. The x-axis component of gravitational acceleration. The gravitational acceleration component along the Y-axis. As the constant of gravitational acceleration, the tilt angles in the two directions together constitute the spatial tilt state of the rigid measuring unit in the monitoring plane.

[0020] Preferably, in step S5, the relative displacement between the rigid measuring units is calculated based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle through geometric projection. Specifically, this involves obtaining the fixed spacing between two adjacent rigid measuring units as... At the initial monitoring moment, the tilt angles of both units were 0°, and they were on the same vertical line. After the dam body shifted, the tilt angle of the upper unit in the X direction became... The tilt angle in the Y direction is The tilt angle of the lower unit in the X direction is The tilt angle in the Y direction is The relative displacement of the two elements in the X direction is calculated using geometric projection relationships. The relative displacement in the Y direction ,in This represents the relative displacement in the X direction. The relative displacement in the Y direction is the resultant displacement of the relative displacements in the two directions. The formula is: To obtain the spatial relative displacement between adjacent rigid measurement units.

[0021] Preferably, in step S6, the relative displacement of each segment is accumulated along the direction of displacement gauge installation to obtain the cumulative displacement value at different depths inside the dam body, forming a complete displacement monitoring profile. Specifically, the rigid measurement units of the displacement gauges are numbered sequentially from the top to the bottom of the dam body. Taking the first unit at the top as the reference point, the cumulative displacement value in the X direction of the i-th unit (i≥2) is... Cumulative displacement value in the Y direction ,in For the first The unit and the first Between units Relative displacement in direction For the first The unit and the first Between units Relative displacement in direction, and the corresponding depth value for each element. , To fix the spacing between adjacent cells, by using each depth value With the corresponding cumulative displacement value , Calculate the resultant displacement value Through the resultant displacement value The total displacement at the depth is obtained, which reveals the spatial distribution characteristics of the displacement inside the dam.

[0022] A MEMS flexible array displacement gauge for monitoring the interior of an earth-rock dam comprises multiple rigid measurement units and flexible connecting units connected alternately. Each rigid measurement unit is a hollow cylindrical structure integrating a triaxial MEMS accelerometer, a data processing module, and a power supply module. Each flexible connecting unit is a bendable strip structure, with both ends fixedly connected to the ends of adjacent rigid measurement units. The connection method involves embedded snap-fits and sealant encapsulation, allowing relative rotation between the rigid measurement units while maintaining good sealing performance. The rigid measurement units are connected end-to-end via the flexible connecting units to form a long strip array structure. Each end of the MEMS flexible array has end fixings, which are threaded to the outer ends of the first and last rigid measurement units. The overall structure can adapt to dam deformation by bending accordingly. The sensing modules of the rigid measurement units are electrically connected via built-in wires through the flexible connecting units, forming a complete data acquisition and transmission link.

[0023] Preferably, the hollow cylindrical structure of the rigid measurement unit has three radially separated chambers: a sensing chamber, a processing chamber, and a power supply chamber. The sensing chamber is located in the middle and houses a triaxial MEMS acceleration sensing module, whose sensing axis maintains a preset angle with the axis of the rigid measurement unit. The processing chamber and the power supply chamber are located on both sides of the sensing chamber. The processing chamber houses a data processing module, and the power supply chamber houses a power supply module. The three chambers are connected by an axially opened wire hole. The end fixing member is a cylindrical structure closed at one end. The closed end has a connecting lug for connecting with an external fixing device, and the inner wall of the open end has an internal thread that matches the outer end of the rigid measurement unit.

[0024] Compared with the prior art, the technical solution of this application has the following technical effects:

[0025] This invention achieves precise monitoring of internal displacement in earth-rock dams through a specific construction, installation, data acquisition, and processing process, combined with a specially designed MEMS flexible array displacement meter. First, boreholes are drilled in a pre-defined monitoring area to ensure the borehole parameters are compatible with the displacement meter. Then, the displacement meter is lowered and fixed by filling it with graded fine sand, allowing the displacement meter to deform synchronously with the dam body. Subsequently, data is collected through the displacement meter's sensors, and after preprocessing, angle calculation, and displacement derivation, the cumulative displacement values ​​at different depths within the dam body are obtained, forming a complete monitoring profile. The matching displacement meter consists of alternating rigid measuring units and flexible connecting units, with rationally partitioned functional modules and fixed at both ends, allowing the overall design to adapt to dam deformation and ensuring stable data transmission.

[0026] The measurement method of this invention has closely linked steps, forming a complete closed loop from construction to monitoring result output. The strict regulations on diameter, axis perpendicularity and depth during drilling construction provide precise space for subsequent displacement gauge installation. The installation method of filling with graded fine sand and vibrating it ensures a rigid connection between the displacement gauge and the dam body, avoiding monitoring errors caused by relative sliding.

[0027] The structural design of the MEMS flexible array displacement gauge of this invention fully considers the complex environment and deformation requirements inside the earth-rock dam. The rigid measurement unit adopts a hollow columnar structure, with three chambers formed by radial division inside, which integrate sensing, processing and power supply modules respectively. The chambers are connected by wire holes, which not only realizes the orderly layout of functional modules, but also ensures the smooth transmission of data and power. The flexible connection unit adopts a bendable strip structure, and the connection method of embedded buckle and sealant sealing allows adjacent rigid measurement units to rotate relative to each other, ensuring that the displacement gauge can flexibly adapt to the bending, settlement and other deformations of the dam body. At the same time, the good sealing performance can resist the erosion of water vapor and impurities inside the dam body. The design of the end fixing part facilitates the connection of the displacement gauge with external devices, improves the overall installation stability, and ensures that the displacement gauge maintains structural integrity and normal function during long-term monitoring.

[0028] This invention effectively meets the practical needs of displacement monitoring inside earth-rock dams, providing key data support for dam safety assessment. Through precise monitoring of displacement at different depths inside the dam, risks such as uneven deformation and potential sliding inside the dam can be detected in a timely manner, providing a basis for engineering maintenance and safety control. The designed displacement gauge structure adapts to the flexible deformation of the dam body, avoiding monitoring interruptions caused by equipment damage, ensuring that the displacement gauge deforms synchronously with the dam body, guaranteeing the authenticity of the monitoring data, and having significant value in improving the monitoring accuracy of earth-rock dams, ensuring monitoring continuity, and enhancing the practicality of the data.

[0029] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.

[0030] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0032] Based on the description of the figures and their corresponding technical content in the document, the titles of the figures are as follows:

[0033] Figure 1 Flowchart of the measurement method for MEMS flexible array displacement gauges in earth-rock dams;

[0034] Figure 2 This is a schematic diagram of the MEMS acceleration signal processing and displacement calculation process.

[0035] Figure 3 This is a schematic diagram of a MEMS flexible array displacement meter structure.

[0036] Figure 4 Schematic diagram of the flexible array displacement gauge arrangement;

[0037] Figure 5 This is a schematic diagram of the sealed chamber structure;

[0038] Figure 6 This is a schematic diagram of the sealant structure for the displacement gauge;

[0039] Figure 7 This is a cross-sectional view of the dam body displacement monitoring in the 20-50m depth range;

[0040] Figure 8 This is a schematic diagram of a homogeneous earth dam structure.

[0041] Figure 9 This is a schematic diagram of an earth-rock hybrid dam structure.

[0042] Figure 10A schematic diagram of the sealing structure (2mm adhesive thickness) for a displacement gauge in a homogeneous earth dam;

[0043] Figure 11 Schematic diagram of the sealing structure (3mm adhesive thickness) for the displacement gauge of a soil-rock mixed dam;

[0044] Figure 12 This is a cumulative displacement monitoring curve for a homogeneous earth dam.

[0045] Figure 13 This is a cumulative displacement monitoring curve for an earth-rock composite dam. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.

[0047] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0048] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.

[0049] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.

[0050] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.

[0051] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.

[0052] Example 1

[0053] This embodiment mainly describes a high-precision MEMS flexible array displacement meter measurement method for monitoring displacement inside earth-rock dams, such as... Figure 1-2 As shown, it includes:

[0054] S1. Drilling is carried out in the pre-set monitoring area of ​​the earth-rock dam; the diameter of the borehole is adapted to the outer diameter of the MEMS flexible array displacement meter, and the borehole axis is kept perpendicular.

[0055] S2. Slowly lower the MEMS flexible array displacement gauge along the borehole so that the rigid measuring units of the MEMS flexible array displacement gauge are evenly distributed at different depths in the borehole. Fill the gap between the borehole and the displacement gauge with graded fine sand and compact it to ensure that the displacement gauge forms a rigid connection with the dam structure and moves synchronously with the deformation of the dam.

[0056] S3. After the fine sand filling stabilizes, the acceleration signal at the location is collected by the triaxial MEMS accelerometer of the rigid measurement unit of the MEMS flexible array displacement meter, and the acceleration data at different times is recorded.

[0057] S4. Preprocess the collected acceleration data, remove outliers and perform smoothing filtering, and calculate the tilt angle of each rigid measurement unit in the monitoring plane based on the gravitational acceleration components.

[0058] S5. Based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle, calculate the relative displacement between the rigid measuring units through geometric projection relationship;

[0059] S6. Accumulate the relative displacement of each segment along the direction of displacement gauge installation to obtain the cumulative displacement value at different depths inside the dam body, forming a complete displacement monitoring profile.

[0060] Furthermore, the drilling depth in S1 is determined based on the dam monitoring requirements. This is achieved through a full-depth monitoring scenario from the dam crest to the dam foundation, specifying the drilling depth. The maximum dam height needs to be covered. Depth of influence of shallow foundation The shallow depth of influence of the dam foundation Based on the internal friction angle of the dam material The difference in water head between the upstream and downstream sides of the dam body and the compression modulus of the dam foundation soil Confirmed, the formula is: ,in .

[0061] Furthermore, in S2, graded fine sand is filled into the gap between the borehole and the displacement gauge and then compacted by vibration. A layered filling method is adopted. First, graded fine sand with a preset thickness is filled into the gap. Then, a vibrating rod with a diameter adapted to the gap width is inserted into the fine sand. The vibrating rod is moved evenly along the circumference of the borehole and vibrated until there is no obvious sinking on the surface of the fine sand. Then, the next layer of graded fine sand is filled. The above filling and vibration are repeated until the gap between the borehole and the displacement gauge is completely filled with graded fine sand.

[0062] Furthermore, the triaxial MEMS accelerometers of each rigid measurement unit in S3 are arranged along the three orthogonal directions of X, Y, and Z, respectively, and the data acquisition frequency of the triaxial MEMS accelerometers is... Based on the dam deformation rate Confirmed, the formula is: ,in This is the proportionality coefficient. This represents the real-time deformation rate of the dam monitoring area. This indicates rounding up, and the sampling frequency increases with the deformation rate.

[0063] Furthermore, in S4, the acquired acceleration data is preprocessed to remove outliers and perform smoothing filtering. Specifically, outliers are identified using the coefficient of variation method, and the coefficient of variation of the acceleration data sequence acquired continuously from the same rigid measurement unit is calculated. The formula is: ,in The mean of the sequence. The standard deviation of a sequence is defined as the absolute value of the deviation of a data point from the mean. It was determined to be an outlier at that time. To predetermine the multiplier, outliers are replaced with the weighted average of three consecutive valid data points. The weights increase linearly with increasing distance. An exponentially weighted moving average is used for smoothing filtering, and the filtering formula is as follows: ,in This is the original data at the current moment. This is the filtering result at the current moment. This is the filtering result from the previous moment. The smoothing coefficient is used to process the acceleration data sequence point by point to obtain a smoothed signal.

[0064] Furthermore, in S4, the tilt angle of each rigid measuring unit in the monitoring plane is calculated based on the gravitational acceleration components. Specifically, the preprocessed acceleration data is analyzed, and the triaxial gravitational acceleration components of each rigid measuring unit in a static state are extracted. The X-axis and Y-axis components reflect the horizontal projection of gravity, and the Z-axis component reflects the vertical projection of gravity. The tilt angle in the X-direction is calculated by the ratio of the X-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: The tilt angle in the Y direction is calculated by the ratio of the Y-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: ,in The tilt angle is in the X direction. The tilt angle in the Y direction. The x-axis component of gravitational acceleration. The gravitational acceleration component along the Y-axis. As the constant of gravitational acceleration, the tilt angles in the two directions together constitute the spatial tilt state of the rigid measuring unit in the monitoring plane.

[0065] Furthermore, in S5, based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle, the relative displacement between the rigid measuring units is calculated through geometric projection relationships. Specifically, the fixed spacing between two adjacent rigid measuring units is obtained as follows: At the initial monitoring moment, the tilt angles of both units were 0°, and they were on the same vertical line. After the dam body shifted, the tilt angle of the upper unit in the X direction became... The tilt angle in the Y direction is The tilt angle of the lower unit in the X direction is The tilt angle in the Y direction is The relative displacement of the two elements in the X direction is calculated using geometric projection relationships. The relative displacement in the Y direction ,in This represents the relative displacement in the X direction. The relative displacement in the Y direction is the resultant displacement of the relative displacements in the two directions. The formula is: To obtain the spatial relative displacement between adjacent rigid measurement units.

[0066] Furthermore, in S6, the relative displacement of each segment is accumulated along the direction of the displacement gauges to obtain the cumulative displacement values ​​at different depths inside the dam, forming a complete displacement monitoring profile. Specifically, the rigid measurement units of the displacement gauges are numbered sequentially from the top to the bottom of the dam. Taking the first unit at the top as the reference point, the cumulative displacement value in the X direction of the i-th unit (i≥2) is... Cumulative displacement value in the Y direction ,in For the first The unit and the first Between units Relative displacement in direction For the first The unit and the first Between units Relative displacement in direction, and the corresponding depth value for each element. , To fix the spacing between adjacent cells, by using each depth value With the corresponding cumulative displacement value , Calculate the resultant displacement value Through the resultant displacement value The total displacement at the depth is obtained, which reveals the spatial distribution characteristics of the displacement inside the dam.

[0067] This embodiment details how to accurately monitor displacement at different depths inside an earth-rock dam, rationally design borehole depths, and combine rigid measuring units with uniform distribution to achieve full-depth coverage. Flexible connection units allow the displacement gauges to flexibly bend with the dam's deformation, and the use of graded fine sand filling and vibration ensures synchronous displacement with the dam, guaranteeing continuous monitoring. Simultaneously, by dynamically adjusting the data acquisition frequency, the cumulative displacement is obtained through preprocessing and geometric calculations, forming a complete monitoring profile that accurately reflects internal deformation. This provides reliable data for dam safety assessment and risk warning, effectively solving the problem of internal displacement monitoring.

[0068] Example 2

[0069] This embodiment describes in detail the use of a MEMS flexible array displacement gauge for monitoring the interior of an earth-rock dam, specifically:

[0070] like Figure 3 As shown, the MEMS flexible array displacement meter consists of multiple rigid measurement units and flexible connection units connected alternately. The rigid measurement unit is a hollow cylindrical structure that integrates a triaxial MEMS accelerometer, a data processing module, and a power supply module. The flexible connection unit is a flexible strip structure, with its two ends fixedly connected to the ends of adjacent rigid measurement units. The connection method is an embedded snap-fit ​​with sealant encapsulation, allowing relative rotation between the rigid measurement units while maintaining good sealing performance. The rigid measurement units are connected end-to-end through the flexible connection units to form a long strip array structure. The MEMS flexible array has end fixing parts at both ends, which are connected to the outer ends of the first and last rigid measurement units by threads. The overall structure can adapt to the deformation of the dam body and bend accordingly. The sensing modules of the rigid measurement units are electrically connected through the flexible connection units via built-in wires, forming a complete data acquisition and transmission link.

[0071] The rigid measurement unit has a hollow cylindrical structure with three radially separated chambers: a sensing chamber, a processing chamber, and a power supply chamber. The sensing chamber is located in the middle and houses a triaxial MEMS accelerometer module, whose sensing axis maintains a preset angle with the axis of the rigid measurement unit. The processing chamber and the power supply chamber are located on either side of the sensing chamber. The processing chamber contains a data processing module, and the power supply chamber contains a power supply module. The three chambers are connected by an axially opened wire hole. The end fixing component is a cylindrical structure closed at one end. The closed end has a connecting lug for connecting to an external fixing device, and the inner wall of the open end has an internal thread that matches the outer end of the rigid measurement unit.

[0072] This embodiment details a MEMS flexible array displacement gauge that uses alternating rigid measurement units and flexible connection units to adaptively bend with the deformation of the dam body, ensuring synchronous displacement with the dam body. The rigid unit integrates sensing, processing, and power supply modules in its internal cavity, working together to ensure accurate data acquisition. The flexible connection uses embedded buckles and sealant encapsulation, combining flexibility and sealing. The end fasteners facilitate installation and fixation. The overall structure enables stable monitoring of displacement at different depths inside the dam body, providing reliable hardware support for accurately acquiring internal deformation data.

[0073] Based on Embodiment 1 or 2, this embodiment details the implementation process and effects of a high-precision MEMS flexible array displacement gauge measurement method for internal displacement monitoring of earth-rock dams at different monitoring depths. Specifically, it takes localized key monitoring of the dam body at a depth range of 20-50m as an example.

[0074] The dam has a maximum height of 60m, a crest width of 10m, and a slope ratio of 1:2.5. It is primarily constructed of silty clay. Localized key monitoring was conducted on the 20-50m depth range of the homogeneous earth dam. Before drilling, ground-penetrating radar was used to determine that the 20-50m range was an area of ​​alternating clay and fine sand layers. This area is prone to uneven deformation due to seepage, hence it was designated as a key monitoring section. The drilling depth was set at 55m, with 20-50m as the core monitoring range and 50-55m as an extension section to ensure data continuity. The borehole diameter was 70mm, matching the outer diameter (50mm) of the MEMS flexible array displacement gauge. An XY-2 geological drilling rig was used, with a tungsten carbide drill bit. The drilling speed was controlled at 0.8m / min. The verticality of the axis was calibrated with an inclinometer every 5m of drilling to ensure a deviation of no more than 0.5°, preventing borehole wall tilting that could obstruct displacement gauge installation.

[0075] Overall embedded structure such as Figure 4 As shown, the MEMS flexible array displacement gauge is 55m long and consists of 110 rigid measuring units and 109 flexible connecting units connected in series alternately; Figure 5As shown, the rigid measurement unit is a hollow cylinder made of 304 stainless steel, with an outer diameter of 50mm, a length of 100mm, and a weight of 200g per unit. Internally, it is divided into a sensing cavity, a processing cavity, and a power supply cavity by radial partitions. The sensing cavity is centrally located and houses a triaxial MEMS accelerometer (model ADXL355). Its X and Y axes are perpendicular to the unit's axis, and its Z axis is parallel to the axis, achieving a resolution of 0.001g. The processing cavity and power supply cavity are located on opposite sides, respectively housing the data processing module and the lithium battery pack (capacity 5000mAh). The cavities are connected by wires through 3mm diameter through-holes. Figure 6 As shown, the flexible connecting unit is a PTFE strip structure, 30mm wide, 5mm thick, and 50mm long. Both ends are connected to the rigid measuring unit via embedded clips with a clip depth of 10mm. It is then encapsulated with silicone rubber sealant (model KR-330) with a 2mm thickness to ensure an IP68 waterproof rating. (See attached image.) Figure 1 As shown in the connection part of the displacement gauge, the flexible structure can rotate relative to the dam body within a range of ±30° as the dam body bends. The end fixing parts at both ends of the displacement gauge are cylindrical structures. The closed end is equipped with two connecting lugs with a diameter of 10mm for fixing to the concrete base (500mm×500mm×300mm) at the orifice. The internal thread (M50×2mm) at the open end matches the external thread of the rigid measuring unit. After installation, the whole structure is flush with the surface of the dam body.

[0076] To improve monitoring accuracy in the 20-50m range, rigid measurement units are densely deployed in this range with an adjacent spacing of 500mm, comprising a total of 60 units (numbered 39-98); the spacing in the 0-20m and 50-55m ranges is 2000mm, with 10 units (numbered 1-10) and 5 units (numbered 99-103) respectively. Figure 4 The distribution of black dots inside the borehole is shown, with denser dots corresponding to key monitoring sections. During installation, first connect the displacement gauge head fixing piece to the borehole base, then slowly lower it using a winch at a speed controlled at 0.5 m / s. Pause for 1 minute every 10 m to check for jamming of the flexible connection unit.

[0077] The gap between the borehole and the displacement gauge is 10mm, filled with graded fine sand (particle size 0.1-0.3mm, mud content ≤3%). Figure 4As shown in the oblique line filling area, the filling is carried out in layers: in the 20-50m section, each layer is 10cm thick, and compacted with an 8mm diameter stainless steel vibrator (model ZX-10). The vibrator is moved every 50mm around the hole, at a frequency of 3000r / min, and each section is compacted for 15s until the surface settlement of the fine sand is ≤1mm within 5s; in other sections, each layer is 20cm thick and compacted for 10s. After filling, the area is left to stand for 48 hours, and the moisture content of the fine sand is monitored by a pre-embedded humidity sensor. Monitoring is started after the moisture content stabilizes at 12%-15% (consistent with the moisture content of the dam soil).

[0078] The data acquisition frequency is dynamically adjusted according to the deformation rate of the dam: the deformation rate is expected to be 0.2 mm / d for the first 3 months, and the frequency is set to 1 Hz; when the rate is >0.5 mm / d, it automatically increases to 10 Hz; when it is <0.1 mm / d, it decreases to 0.5 Hz. The sensor generates a data packet once per hour, which includes triaxial acceleration values, timestamps, battery voltage (≥3.6V is normal) and temperature (-10℃-60℃).

[0079] The coefficient of variation method is used to identify outliers, and the mean is calculated for 100 consecutive sets of data. and standard deviation When the data deviation is >2.8×( / )× If an anomaly is detected, it is replaced with the weighted average of the three preceding and following valid data points (weights set to 0.5, 0.3, and 0.2 based on distance); then, it is smoothed using an exponentially weighted moving average filter with a smoothing coefficient. =0.3, that is, the current filter value = 0.3 × original value + 0.7 × previous filter value, which effectively eliminates high-frequency noise generated by drilling vibration.

[0080] The tilt angle calculation is based on the preprocessed gravitational acceleration components: X-direction tilt angle = arcsin(X-axis component / g), and the same applies to the Y-direction. Taking units numbered 50 (depth 25.5m), 60 (30.5m), 70 (35.5m), 80 (40.5m), and 90 (45.5m) as examples, the X-direction tilt angles on the 30th day are 0.12°, 0.15°, 0.11°, 0.18°, and 0.14°, respectively, and the Y-direction tilt angles are 0.08°, 0.10°, 0.09°, 0.13°, and 0.11°, respectively.

[0081] The relative displacement was calculated using geometric projection: the distance between adjacent elements L = 500mm (key area), the relative displacement in the X direction = L × [sin(lower element tilt angle) - sin(upper element tilt angle)], and the same applies to the Y direction. The calculations show that the displacement between elements 50 and 51 is 0.8mm in the X direction and 0.5mm in the Y direction, totaling 0.94mm; the displacement between elements 80 and 81 is 1.2mm in the X direction and 0.7mm in the Y direction, totaling 1.39mm, indicating significant deformation at 40.5m.

[0082] The cumulative displacement was taken as the baseline with point 1 (depth 0m). Point 39 (20m) had a displacement of 12.3mm in the X direction and 8.5mm in the Y direction; point 69 (35m) had a displacement of 28.7mm in the X direction and 19.2mm in the Y direction; and point 98 (50m) had a displacement of 42.5mm in the X direction and 27.6mm in the Y direction. These data were plotted into a displacement monitoring profile, as shown below. Figure 7 As shown, the slope of the curve increases in the 35-40m range, corresponding to the boundary between the clay and sand layers marked in the figure, which is consistent with the geological survey results, indicating that the deformation in this range is significantly affected by the stratigraphic interface.

[0083] This embodiment describes in detail that the application achieves high-precision monitoring in the 20-50m range. The encrypted rigid measurement unit and targeted installation and processing methods ensure accurate capture of deformation details, provide reliable data support for risk assessment in the middle of the dam body, and clearly identify areas of abnormal deformation.

[0084] Based on Embodiment 1 or 2, this embodiment details the implementation process and effects of a high-precision MEMS flexible array displacement meter measurement method for monitoring displacement inside earth-rock dams under different dam material properties. Specifically, it selects material compatibility monitoring for homogeneous earth dams and earth-rock hybrid dams, as follows:

[0085] The homogeneous earth dam is located in the humid southern region. It is 45m high, 8m wide at the top, and has a slope ratio of 1:2.2. It is mainly composed of silty clay (internal friction angle 22°, compression modulus 8MPa), and the foundation is a clay layer. The earth-rock mixed dam is located in the semi-arid northern region. It is 50m high, 10m wide at the top, and has a slope ratio of 1:2.5. It is filled with a mixture of gravel (60%) and silty clay (40%) (internal friction angle 35°, compression modulus 18MPa), and the foundation contains a pebble layer.

[0086] The two MEMS flexible array displacement gauges, each 40m in length, consist of 80 rigid measuring units and 79 flexible connecting units. Figure 8 The image shows a scenario for installing a homogeneous earth dam. Figure 9The diagram shows a mixed earth-rock dam. The rigid measuring unit is a hollow 316 stainless steel cylinder with an outer diameter of 55mm, a length of 120mm, and a weight of 220g. Internally, it is divided into a sensing chamber, a processing chamber, and a power supply chamber by radial partitions. The sensing chamber houses an ADXL355 triaxial accelerometer (X and Y axes perpendicular to the axis, Z axis parallel), with a resolution of 0.001g. The processing chamber contains an STM32L476 processor, and the power supply chamber is a 10000mAh lithium battery. The diameter of the wire passage between the chambers is 4mm. The flexible connecting unit is a fluororubber strip structure (35mm wide, 6mm thick, 60mm long), with 12mm deep embedded buckles at both ends, encapsulated with silicone rubber sealant. Figure 10 As shown, the displacement gauge (No. A) for homogeneous earth dams uses a 2mm thick sealant, suitable for low-permeability cohesive soils; (The rest of the text appears to be unrelated and possibly machine-generated gibberish.) Figure 11 As shown, the sealant thickness of the displacement gauge (No. B) used in the earth-rock hybrid dam is 3mm to enhance its resistance to abrasion from sand and gravel. The thicknesses of the two sealants are marked with different shades of gray.

[0087] For the homogeneous earth dam (No. A), the borehole diameter was 65mm, the depth was 42m, and an XY-1 drilling rig was used with a drilling speed of 0.6m / min. The verticality was calibrated every 3m (deviation ≤0.4°). The gap between the borehole and the displacement gauge was 10mm. Graded fine sand (particle size 0.3-0.5mm, mud content ≤2%, dry density 1.5g / cm³) was filled in layers 15cm thick. The sand was compacted using an 8mm diameter titanium alloy vibrator (ZX-15) at a frequency of 2500r / min for 10s per section, until the surface of the fine sand settled ≤0.5mm within 5s. After filling, the dam was allowed to stand for 72 hours. Monitoring was initiated after the TDR moisture sensor showed that the moisture content stabilized at 18%-20% (matching the dam body clay).

[0088] For the earth-rock mixed dam (No. B), the borehole diameter is 70mm, the depth is 55m, and an XY-3 drilling rig with a gold-tooth drill bit is used. The drilling speed is 1.0m / min, and the verticality is calibrated every 2m (deviation ≤0.3°). The gap is 15mm, and graded fine sand (particle size 0.2-0.4mm, mud content ≤1%, dry density 1.7g / cm³) is filled in layers 10cm thick. A 10mm diameter tungsten carbide vibrator (ZX-20) is used for compaction at a frequency of 3500r / min for 15s at each location, ensuring that the fine sand penetrates into the gravel gaps and that the surface settlement is ≤0.3mm / 5s. After filling, the dam is allowed to stand for 48 hours. Once the moisture content stabilizes at 10%-12% (matching the gravel layer), monitoring is initiated.

[0089] For a homogeneous earth dam (No. A), the cohesive soil deforms slowly. The initial sampling frequency was 0.5 Hz, increasing to 2 Hz when the rate exceeded 0.3 mm / d. Outlier identification was performed using the coefficient of variation method (k=3.0). Outliers exceeding 3.0 × CV × 10⁻⁶ were identified in 80 consecutive data sets. When the time is right, replace the data with a weighted average of the three preceding and following data (weights 0.6, 0.3, and 0.1); smoothing filter. =0.2 (current value = 0.2 × original value + 0.8 × previous value), weakening high-frequency noise. Data packets are generated every 30 minutes, including triaxial acceleration (±0.002g), temperature (-20℃-70℃), battery voltage (3.3-4.2V), etc., and transmitted via LoRa.

[0090] For the earth-rock composite dam (No. B), the interface is prone to abrupt deformation. The initial frequency is 2Hz, and it rises to 10Hz when the velocity exceeds 0.8mm / d. Outlier identification k=2.5, and the deviation exceeds 2.5×CV× in 60 consecutive sets of data. Time-based replacement (weights 0.5, 0.3, 0.2); smoothing filter =0.4 (current value = 0.4 × original value + 0.6 × previous value), retaining mutation characteristics.

[0091] Obtain the monitoring results and conduct a correlation analysis with material properties, specifically:

[0092] For a homogeneous earth dam (No. A), after 60 days of operation, the X-direction tilt angles at depths of 10m (clay layer, No. 15), 25m (clay layer, No. 40), and 40m (dam foundation clay, No. 75) are 0.08°, 0.11°, and 0.07°, respectively, and the Y-direction tilt angles are 0.05°, 0.09°, and 0.06°, respectively. Relative displacements: No. 15-16: X-direction 0.5mm, Y-direction 0.3mm (total displacement 0.58mm); No. 40-41: X-direction 0.7mm, Y-direction 0.5mm (total displacement 0.86mm). The cumulative displacement at 40m is 18.2mm in the X-direction and 11.5mm in the Y-direction (total displacement 21.5mm), as shown in the attached diagram. Figure 12 As shown, the overall surface is flat, consistent with the uniform deformation characteristics of cohesive soil.

[0093] For the earth-rock mixed dam (No. B), after 60 days of operation, the X-direction tilt angles at depths of 15m (gravel layer, No. 20), 30m (interface, No. 50), and 50m (pebble layer, No. 80) are 0.15°, 0.22°, and 0.13°, respectively, and the Y-direction tilt angles are 0.10°, 0.18°, and 0.09°, respectively. Relative displacements: No. 20-21: X-direction 1.1mm, Y-direction 0.7mm (total displacement 1.30mm); No. 50-51: X-direction 1.8mm, Y-direction 1.2mm (total displacement 2.16mm), with significant interface deformation. The cumulative displacement at 50m is 35.6mm in the X-direction and 22.3mm in the Y-direction (total displacement 42.1mm), as shown in the attached diagram. Figure 13 As shown, the slope abruptly changes at 30m, corresponding to the marked "clay layer / gravel layer" interface, reflecting the shear deformation caused by the material difference.

[0094] After six months of operation, the sealant integrity rate of displacement gauge A was 98%, while that of displacement gauge B, due to its thickened design, reached 97% (compared to approximately 90% for standard gauges), with no water leakage or damage. Comparison with total station data showed an error of ≤2%, verifying the effectiveness of the adaptability design. (See attached data.) Figure 8 The curve on the left is labeled "maximum resultant displacement 21.5mm", and the curve on the right at 30m is labeled "resultant displacement at interface 2.16mm". The data points are marked with square (homogeneous) and circle (mixed) shapes, clearly showing the influence of materials on deformation.

[0095] This embodiment achieves precise monitoring of the material property differences between homogeneous earth dams and earth-rock hybrid dams through customized design. The homogeneous earth dam scheme is adapted to the low-abrasion cohesive soil environment, and the monitoring curve is flat, fully presenting the uniform deformation characteristics. The earth-rock hybrid dam scheme enhances the resistance to sand and gravel abrasion and clearly captures the deformation abrupt changes at the material interface. Both schemes maintain high stability through the method of this application, reflecting the deformation law of different dam bodies, providing reliable technical support for differentiated safety assessment, and verifying the practicality of the adaptability design.

[0096] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter changes made to these embodiments within the spirit and principles of the present invention, without departing from the principles and spirit of the present invention, through conventional substitutions or to achieve the same function, fall within the scope of protection of the present invention.

Claims

1. A high-precision MEMS flexible array displacement meter measurement method for monitoring displacement inside earth-rock dams, characterized in that, include: S1. Drilling is carried out in the pre-set monitoring area of ​​the earth-rock dam; the diameter of the borehole is adapted to the outer diameter of the MEMS flexible array displacement meter, and the borehole axis is kept perpendicular. S2. Slowly lower the MEMS flexible array displacement gauge along the borehole so that the rigid measuring units of the MEMS flexible array displacement gauge are evenly distributed at different depths in the borehole. Fill the gap between the borehole and the displacement gauge with graded fine sand and compact it to ensure that the displacement gauge forms a rigid connection with the dam structure and moves synchronously with the deformation of the dam. S3. After the fine sand filling stabilizes, the acceleration signal at the location is collected by the triaxial MEMS accelerometer of the rigid measurement unit of the MEMS flexible array displacement meter, and the acceleration data at different times is recorded. S4. Preprocess the collected acceleration data, remove outliers and perform smoothing filtering, and calculate the tilt angle of each rigid measurement unit in the monitoring plane based on the gravitational acceleration components. S5. Based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle, calculate the relative displacement between the rigid measuring units through geometric projection relationship; S6. Accumulate the relative displacement of each segment along the direction of displacement gauge installation to obtain the cumulative displacement value at different depths inside the dam body, forming a complete displacement monitoring profile. The MEMS flexible array displacement meter is composed of multiple rigid measurement units and flexible connection units connected alternately. The rigid measurement unit is a hollow cylindrical structure that integrates a triaxial MEMS acceleration sensing module, a data processing module, and a power supply module. The flexible connection unit is a flexible strip structure, with its two ends fixedly connected to the ends of adjacent rigid measurement units. The connection method is an embedded snap-fit ​​with sealant encapsulation, which allows the rigid measurement units to rotate relative to each other while maintaining good sealing performance. The rigid measurement units are connected end-to-end through the flexible connection units to form a long strip array structure. The MEMS flexible array has end fixing parts at both ends, which are connected to the outer ends of the first and last rigid measurement units through threads. The overall structure can bend adaptively with the deformation of the dam body. The sensing modules of the rigid measurement units are electrically connected through the flexible connection units via built-in wires, forming a complete data acquisition and transmission link. The rigid measurement unit has a hollow cylindrical structure with three radially separated chambers: a sensing chamber, a processing chamber, and a power supply chamber. The sensing chamber is located in the middle and houses a triaxial MEMS acceleration sensing module, whose sensing axis maintains a preset angle with the axis of the rigid measurement unit. The processing chamber and the power supply chamber are located on either side of the sensing chamber. The processing chamber contains a data processing module, and the power supply chamber contains a power supply module. The three chambers are connected by an axially opened wire hole. The end fixing component is a cylindrical structure closed at one end. The closed end has a connecting lug for connecting to an external fixing device, and the inner wall of the open end has an internal thread that matches the outer end of the rigid measurement unit.

2. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, The drilling depth in S1 is determined based on the dam monitoring requirements. This is achieved through a full-depth monitoring scenario from the dam crest to the dam foundation. The maximum dam height needs to be covered. Depth of influence of shallow foundation The shallow depth of influence of the dam foundation Based on the internal friction angle of the dam material The difference in water head between the upstream and downstream sides of the dam body and the compression modulus of the dam foundation soil Confirmed, the formula is ,in .

3. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, In step S2, graded fine sand is filled into the gap between the borehole and the displacement gauge and then compacted by vibration. A layered filling method is adopted. First, graded fine sand with a preset thickness is filled into the gap. Then, a vibrating rod with a diameter adapted to the gap width is inserted into the fine sand. The vibrating rod is moved evenly along the circumference of the borehole and vibrated until there is no obvious sinking on the surface of the fine sand. Then, the next layer of graded fine sand is filled. The above filling and vibration are repeated until the gap between the borehole and the displacement gauge is completely filled with graded fine sand.

4. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, The triaxial MEMS accelerometers of each rigid measurement unit in S3 are arranged along the three orthogonal directions of X, Y, and Z, respectively. The data acquisition frequency of the triaxial MEMS accelerometers is... Based on the dam deformation rate Confirmed, the formula is: ,in This is the proportionality coefficient. This represents the real-time deformation rate of the dam monitoring area. This indicates rounding up, and the sampling frequency increases with the deformation rate.

5. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, In step S4, the collected acceleration data is preprocessed to remove outliers and perform smoothing filtering. Specifically, outliers are identified using the coefficient of variation method, and the coefficient of variation of the acceleration data sequence continuously collected from the same rigid measurement unit is calculated. The formula is: ,in The mean of the sequence. The standard deviation of a sequence is defined as the absolute value of the deviation of a data point from the mean. It was determined to be an outlier at that time. To predetermine the multiplier, outliers are replaced with the weighted average of three consecutive valid data points. The weights increase linearly with increasing distance. An exponentially weighted moving average is used for smoothing filtering, and the filtering formula is as follows: ,in This is the original data at the current moment. This is the filtering result at the current moment. This is the filtering result from the previous moment. The smoothing coefficient is used to process the acceleration data sequence point by point to obtain a smoothed signal.

6. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, In step S4, the tilt angle of each rigid measuring unit in the monitoring plane is calculated based on the gravitational acceleration components. Specifically, the preprocessed acceleration data is analyzed, and the triaxial gravitational acceleration components of each rigid measuring unit in a static state are extracted. The X-axis and Y-axis components reflect the horizontal projection of gravity, and the Z-axis component reflects the vertical projection of gravity. The tilt angle in the X-direction is calculated by the ratio of the X-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: The tilt angle in the Y direction is calculated by the ratio of the Y-axis gravitational acceleration component to the gravitational acceleration value, using the following formula: ,in The tilt angle is in the X direction. The tilt angle in the Y direction. The x-axis component of gravitational acceleration. The gravitational acceleration component along the Y-axis. As the constant of gravitational acceleration, the tilt angles in the two directions together constitute the spatial tilt state of the rigid measuring unit in the monitoring plane.

7. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, In step S5, the relative displacement between rigid measuring units is calculated based on the fixed spacing between adjacent rigid measuring units and the calculated tilt angle using geometric projection relationships. Specifically, the fixed spacing between two adjacent rigid measuring units is obtained as follows: At the initial monitoring moment, the tilt angles of both units were 0°, and they were on the same vertical line. After the dam body shifted, the tilt angle of the upper unit in the X direction became... The tilt angle in the Y direction is The tilt angle of the lower unit in the X direction is The tilt angle in the Y direction is The relative displacement of the two elements in the X direction is calculated using geometric projection relationships. The relative displacement in the Y direction ,in This represents the relative displacement in the X direction. The relative displacement in the Y direction is the resultant displacement of the relative displacements in the two directions. The formula is: To obtain the spatial relative displacement between adjacent rigid measurement units.

8. The high-precision MEMS flexible array displacement meter measurement method for monitoring internal displacement of earth-rock dams according to claim 1, characterized in that, In step S6, the relative displacement of each segment is accumulated along the direction of the displacement gauges to obtain the cumulative displacement value at different depths inside the dam, forming a complete displacement monitoring profile. Specifically, the rigid measurement units of the displacement gauges are numbered sequentially from the top to the bottom of the dam. Taking the first unit at the top as the reference point, the cumulative displacement value in the X direction of the i-th unit (i≥2) is... Cumulative displacement value in the Y direction ,in For the first The unit and the first Between units Directional relative displacement For the first The unit and the first Between units Relative displacement in direction, and the corresponding depth value for each element. , To fix the spacing between adjacent cells, by using each depth value With the corresponding cumulative displacement value , Calculate the resultant displacement value Through the resultant displacement value The total displacement at the depth is obtained, which reveals the spatial distribution characteristics of the displacement inside the dam.

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