Intelligent strain gauge drilling inclinometer and measurement method

Abstract

The present invention provides an intelligent strain-type borehole inclinometer, comprising an inclinometer outer tube, a plurality of force transmission sheets, a strain rod and a detection circuit. The two ends of the inclinometer outer tube are sealed, and all the force transmission sheets are arranged inside the inclinometer outer tube. The inclinometer outer tube is spaced into a plurality of strain units along the axial interval distribution. The strain rod is arranged on the axis of the inclinometer outer tube, penetrates and is fixedly connected to all the force transmission sheets. Four resistance strain gauges are arranged in each strain unit. The four strain gauges are fixed to the outer wall of the strain rod and are evenly distributed around the outer wall of the strain rod. The detection circuit is respectively connected to the four strain gauges of each strain unit. The detection circuit is used to obtain electrical signals from the four strain gauges of each strain unit, and calculate the displacement corresponding to the landslide section corresponding to each strain unit according to these electrical signals. The beneficial effects of the present invention are as follows: the time interval of data acquisition can be adjusted to obtain real-time data of deep displacement of the landslide, and the deep displacement monitoring data of the landslide body obtained is continuous in space.

Description

Technical Field

[0001] The present invention relates to the technical field of geological disaster monitoring, and in particular to an intelligent strain-type borehole inclinometer and a measuring method. Background Art

[0002] Geological disaster monitoring is an important means of obtaining the changes and development of geological disasters, and is an important part of geological disaster prediction and forecasting. Deep displacement monitoring is one of the core contents of geological disaster monitoring, and is the main means to examine the deformation and change characteristics of the internal material of the landslide under its own gravity and external forces. Deep displacement monitoring is an important method for analyzing the location of the landslide sliding zone, the deformation mechanism and movement characteristics of the landslide, and plays a key role in the success of geological disaster prediction and forecasting.

[0003] At present, the deep displacement monitoring of landslide mainly uses borehole inclinometers. The method is to set up several monitoring points on the landslide, use a drilling rig to drill through the sliding body until a certain depth in the sliding bed, and set up an inclinometer tube with a guide groove in the borehole. When monitoring the deep displacement of the landslide, the inclinometer is placed at the bottom of the borehole, and gradually moves from the bottom of the borehole to the top along the guide groove to obtain information on the spatial angle change of the inclinometer tube, and obtain the displacement of the rock and soil body at different parts deep in the landslide body.

[0004] The existing borehole inclinometers have the following problems: ① The inclinometer does not collect angle change data at full depth in the inclinometer tube, but collects data from the angle sensor according to a set unit distance. Therefore, there is a large error in inferring the deformation of a borehole based on the data collected at one point in space. ② The data collection of the inclinometer is discontinuous in time. Since many landslides deform slowly, in engineering practice, periodic monitoring is often used, that is, monitoring is carried out at regular intervals, making it difficult to obtain continuous landslide deformation data. Summary of the invention

[0005] In view of this, an embodiment of the present invention provides an intelligent strain gauge drilling inclinometer and a measurement method.

[0006] An embodiment of the present invention provides an intelligent strain-type borehole inclinometer, comprising an inclinometer outer tube, a plurality of force transmission sheets, a strain rod and a detection circuit. The inclinometer outer tube is sealed at both ends, the force transmission sheet is in a circular ring shape, all the force transmission sheets are arranged inside the inclinometer outer tube, and the side wall of each of the force transmission sheets is in contact with and fixedly connected to the inner wall of the inclinometer outer tube. All the force transmission sheets are spaced apart along the axial direction to separate the inclinometer outer tube into a plurality of strain units. The strain rod is arranged on the axis of the inclinometer outer tube, penetrates through and is fixedly connected to all the force transmission sheets. Four resistance strain sheets are arranged in each of the strain units, the four strain sheets are fixed to the outer wall of the strain rod and are evenly distributed around the outer wall of the strain rod, all the strain sheets on the strain rod are arranged into four busbars of the strain rod, the detection circuit is respectively connected to the four strain sheets of each of the strain units, and the detection circuit is used to obtain electrical signals from the four strain sheets of each of the strain units, and calculate the displacement corresponding to the landslide section corresponding to each of the strain units according to the electrical signals.

[0007] Furthermore, the surface of each of the force transmission plates is provided with four reinforcing ribs distributed in a cross shape.

[0008] Furthermore, all the force transmission sheets are evenly distributed along the axial direction of the inclinometer outer tube, and the axial distance between the strain sheets of two adjacent strain units is equal to the length of the strain unit.

[0009] Furthermore, each of the strain units is 1 m in length.

[0010] An embodiment of the present invention further provides a strain gauge drilling inclination measurement method, which uses the above-mentioned intelligent strain gauge drilling inclinometer and includes the following steps:

[0011] S1 predicts the main sliding direction of the landslide, and arranges the inclinometer outer tube in a borehole on the landslide so that two strain gauges opposite to each other of the strain unit are arranged along the predicted main sliding direction;

[0012] S2: the sliding of the landslide causes the inclinometer outer tube to bend, the strain rod and the inclinometer outer tube to bend synchronously, and the four strain gauges in each strain unit are deformed to generate electrical signals;

[0013] S3 The detection circuit calculates the microstrain of each strain gauge from the relationship between resistance and strain, and numbers the strain units of the inclinometer outer tube. The strain unit at the bottom is numbered 1, and the number increases upwards. The strain gauge direction of strain unit i along the main sliding direction is defined as the x+ direction, and the microstrain generated is ε x+i , i = 1, 2, 3, ..., the strain gauge direction opposite to the main sliding direction is defined as the x-direction, and the microstrain generated is ε x-i , there is ε x+i +ε x-i= 0, the direction of the strain gauge along the main sliding direction + counterclockwise rotation of 90° is defined as the y+ direction, and the microstrain generated is ε y+i , the direction of the strain gauge rotated 90° clockwise along the main sliding direction is defined as the y-direction, and the microstrain generated is ε y-i , there is ε y+i +ε y-i =0;

[0014] S4 calculates the displacement of each strain unit according to the geometric relationship, specifically:

[0015] x-direction:

[0016]

[0017] y direction:

[0018]

[0019] Total displacement:

[0020]

[0021] Where:

[0022] θ is the central angle of the strain rod of the strain unit after bending;

[0023] r is the cross-sectional radius of the strain bar;

[0024] l is the original length of the strain bar of the strain unit;

[0025] Δ xi is the horizontal displacement in the x+ direction at the upper end point of the strain bar of the strain unit;

[0026] Δ yi is the horizontal displacement in the y+ direction at the upper end point of the strain bar of the strain unit;

[0027] Δ i is the combined horizontal displacement in the x+ direction and the y+ direction at the upper end point of the strain rod of the strain unit;

[0028] Furthermore, it also includes S5, calculating the displacement of the strain bar, which is as follows:

[0029] Cumulative horizontal displacement in the x direction:

[0030]

[0031] Cumulative horizontal displacement in the y direction:

[0032]

[0033] Cumulative total horizontal displacement

[0034]

[0035] Where:

[0036] n is the number of strain units;

[0037] Δ x is the cumulative displacement in the x direction;

[0038] Δ y is the cumulative displacement in the y direction;

[0039] Δ is the cumulative displacement of the strain bar in the horizontal plane.

[0040] Furthermore, it also includes S6, setting the angle between the microstrain in the x+ direction of the strain unit i and the actual main sliding direction of the landslide to α i ,but

[0041]

[0042] Then the degree of deviation between the actual main sliding direction of the landslide and the x+ direction can be calculated by the following formula:

[0043]

[0044] Where:

[0045] R i is the curvature radius of the strain rod of variable unit i after bending;

[0046] θ i is the central angle of the bending section of the strain rod of variable unit i.

[0047] The technical solution provided by the embodiment of the present invention has the following beneficial effects:

[0048] ① According to the monitoring accuracy requirements, the time interval of data collection can be adjusted independently to obtain real-time data of deep displacement of landslide;

[0049] ② Since the strain rod is a rigid rod, the deformation of the strain rod can be calculated according to the material mechanical characteristics of the strain rod, so the deep displacement monitoring data of the landslide body obtained is continuous in space;

[0050] ③The range of deep landslide displacement monitoring is greater than that of existing borehole inclinometers;

[0051] ④ The landslide deformation warning threshold can be preset. When the landslide deformation reaches the threshold, the landslide warning is triggered intelligently to provide warning information to decision-making departments and people within the landslide impact area;

[0052] ⑤ Use automated and intelligent electronic monitoring equipment to reduce personnel workload and improve early warning efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a structural schematic diagram of an intelligent strain gauge drilling inclinometer of the present invention;

[0054] Figure 2 yes Figure 1 Schematic diagram of the structure of the middle force transmission plate;

[0055] Figure 3 is a schematic diagram of the bending of the strain bar;

[0056] Figure 4 This is a schematic diagram of the displacement calculation principle of the bending section of the strain bar;

[0057] Figure 5 This is a schematic diagram of the calculation of the angle between the x+ direction and the actual main sliding direction.

[0058] In the figure: 1- inclinometer outer tube, 2- end cover, 3- force transmission plate, 4- strain rod, 5- strain gauge, 6- reinforcing rib, 7- strain unit. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0060] Please refer to Figure 1 An embodiment of the present invention provides an intelligent strain-type drilling inclinometer, including an inclinometer outer tube 1, a plurality of force transmission sheets 3, a strain rod 4 and a detection circuit.

[0061] Please refer to Figure 2 The inclinometer outer tube 1 is a cylindrical body, with both ends open and provided with end caps 2, and the two end caps 2 seal the two ends of the inclinometer outer tube 1 respectively. The length of the inclinometer outer tube 1 is consistent with the depth of the borehole, and the inclinometer outer tube 1 can withstand a certain bending moment and shear force without damage. The force transmission plate 3 is circular, and the force transmission plate 3 here is specifically a circular ring, whose outer diameter is equal to the inner diameter of the inclinometer outer tube 1, and the inner diameter is equal to the diameter of the strain rod 4. Four reinforcing ribs 6 are provided on the surface of the force transmission plate 3, and the four reinforcing ribs 6 are evenly arranged around the inner hole of the force transmission plate 3 and arranged in a cross shape.

[0062] All the force transmission plates 3 are arranged inside the inclinometer outer tube 1, and the side wall of each of the force transmission plates 3 is attached to and fixedly connected with the inner wall of the inclinometer outer tube 1. All the force transmission plates 3 are distributed at intervals along the axial direction to divide the inclinometer outer tube 1 into a plurality of strain units 7. All the force transmission plates 3 are evenly distributed along the axial direction of the inclinometer outer tube 1, so that the length of each of the strain units 7 is the same.

[0063] The strain rod 4 is arranged on the axis of the inclinometer outer tube 1, and penetrates and is fixedly connected to the inner holes of all the force transmission sheets 3. Four resistance strain gauges 5 are arranged in each strain unit 7. The four strain gauges 5 are fixed to the outer wall of the strain rod 4 by bonding, and the four strain gauges 5 are evenly distributed around the outer wall of the strain rod 4, dividing the circumference of the strain rod 4 into four equal parts. In this embodiment, the four strain gauges 5 are arranged on the strain rod in the middle of the strain unit 7, so that the axial distance between the strain gauges 5 of two adjacent strain units 7 is equal to the length of the strain unit 7. In engineering practice, the length of the strain unit 7 is generally 1m. All the strain gauges 5 on the strain rod 4 are arranged into four busbars of the strain rod 4, that is, the four strain gauges 5 of any strain unit 7 are aligned one by one with the four strain gauges 5 of the adjacent strain unit 7 in the axial direction and are located on the same straight line.

[0064] In this embodiment, the material of the strain rod 4 is selected from high-quality alloy aluminum, which has a high yield strength, ensuring the measuring range of the inclinometer and reducing the influence of its own rod weight on the rod strain; the strain rod 4 has good elasticity and a consistent elastic modulus at all locations. When elastic deformation occurs, the deformation amount can be accurately calculated.

[0065] The detection circuit is respectively connected to the four strain gauges 5 of each strain unit 7. The inclinometer outer tube 1 bends and deforms under the influence of the landslide deformation force, forcing the strain rod 4 to bend and deform synchronously. The strain gauge 5 deforms to generate an electrical signal. The detection circuit detects the electrical signals generated by the four strain gauges 5 of each strain unit 5, and calculates the displacement corresponding to the landslide section corresponding to each strain unit 7 based on these electrical signals.

[0066] An embodiment of the present invention further provides a strain gauge drilling inclination measurement method, which uses the above-mentioned intelligent strain gauge drilling inclinometer and includes the following steps:

[0067] S1: predicting the main sliding direction of the landslide according to the engineering geological conditions of the landslide, arranging the inclinometer outer tube 1 in the borehole on the landslide, so that the two strain gauges 5 opposite to each other of the strain unit 7 are arranged along the predicted main sliding direction, so that the other two strain gauges 5 of the strain unit 7 are located in the vertical direction of the predicted main sliding direction; filling fine sand between the inclinometer outer tube 1 and the hole wall, and making it dense;

[0068] S2 When the landslide slides, the sliding of the landslide causes the inclinometer outer tube 1 to bend, and the force transmission sheet 3 transmits the force to the strain rod 4. The strain rod 4 is subjected to the force and bends synchronously with the inclinometer outer tube 1, so that the strain gauge 5 is deformed, and the four strain gauges 5 in each strain unit 7 are deformed to generate an electrical signal;

[0069] S3 The detection circuit calculates the microstrain of each strain gauge 5 from the relationship between resistance and strain, and numbers the strain units 7 of the inclinometer outer tube 1. The strain unit 7 at the bottom is numbered 1, and the number increases upwards. The direction of the strain gauge 5 of the strain unit i along the main sliding direction is defined as the x+ direction, and the microstrain generated is ε x+i , i = 1, 2, 3, ..., define the direction of the strain gauge 5 opposite to the main sliding direction as the x-direction, and the microstrain generated is ε x-i , there is ε x+i +ε x-i = 0, the direction of the strain gauge rotated 90° counterclockwise along the main sliding direction is defined as the y+ direction, and the microstrain generated is ε y+i , the direction of the strain gauge rotated 90° clockwise along the main sliding direction is defined as the y-direction, and the microstrain generated is ε y-i , there is ε y+i +ε y-i =0;

[0070] When the landslide deforms, the strain rod 4 bends and deforms under the influence of the deformation force of the landslide, and the side facing away from the main sliding direction is pulled, and the surface of the rod body is elongated. The strain value measured by each strain gauge is the ratio of the elongation of the strain rod 4 to the original length. The strain rod 4 bends under the force of the landslide, and compresses and deforms on one side along the displacement direction of the landslide, and stretches and deforms on the side opposite to the displacement direction of the landslide. The displacement value fed back by the strain gauge 5 is two positive and two negative, or one positive, one negative and two zero.

[0071] Since the strain rod 4 is an elastic rod, the deformations produced by the two opposite strain gauges 5 are the same, i.e., ε x+i With ε x-i The value is the same, ε x-i Tension is positive, ε x+i The pressure is negative; ε y+i With ε y-i The same value, one positive and one negative, or ε y+i =ε y+i = 0, but ε y+i With ε y-i The positive and negative directions of and the x+ direction are related to the deviation angle of the main sliding direction.

[0072] S3 calculates the displacement of each strain unit 7 according to the geometric relationship, specifically:

[0073] Please refer to Figure 3 First, the bending deformation of the strain rod 4 is analyzed. For a bending section of the strain rod 4, the geometric relationship can be obtained.

[0074]

[0075] Where:

[0076] ε is the strain measured by strain gauge 5;

[0077] R is the curvature radius of the strain rod 4 after bending (m);

[0078] θ is the central angle corresponding to the bending section of the strain rod 4 (°);

[0079] r is the radius of the strain bar 4 section (m);

[0080] l is the original length of the bending section of the strain rod 4 (m).

[0081] Please refer to Figure 4 , the displacement of the end point of the bending section of the strain rod 4 can be further calculated as:

[0082]

[0083] Where:

[0084] dΔ is the horizontal displacement (m) at the end point of a bending section of the strain rod 4.

[0085] The spatial displacement of the borehole where the inclinometer is located can be obtained by integrating each displacement segment, and the formula is as follows:

[0086]

[0087] Where:

[0088] Δ is the cumulative horizontal displacement of the strain rod 4 (m).

[0089] The bending deformation of the strain gauge in each strain unit is the same as the bending deformation of the bending section of the strain rod, so the displacement of each strain gauge is:

[0090] x-direction:

[0091]

[0092] y direction:

[0093]

[0094] Total displacement:

[0095]

[0096] Where:

[0097] θ is the central angle (°) corresponding to the bending of the strain rod 4 in the strain unit 7;

[0098] r is the cross-sectional radius of the strain bar (m);

[0099] ; is the length of the strain rod 4 in the strain unit 7 (m).

[0100] Δ xi is the horizontal displacement in the x+ direction at the upper end point of the strain rod 4 in the strain unit 7 (m).

[0101] Δ yi is the horizontal displacement in the y+ direction at the upper end point of the strain rod 4 in the strain unit 7 (m).

[0102] Δ i It is the combined horizontal displacement in the x+ direction and the y+ direction at the upper end point of the strain rod 4 in the strain unit 7 (m).

[0103] S4, calculating the overall displacement of the strain bar 4, specifically as follows,

[0104] Cumulative horizontal displacement in the x direction:

[0105]

[0106] Cumulative horizontal displacement in the y direction:

[0107]

[0108] Cumulative total horizontal displacement

[0109]

[0110] Where:

[0111] n is the number of strain units 7;

[0112] Δ x is the cumulative displacement in the x direction (m);

[0113] Δ y is the cumulative displacement in the y direction (m);

[0114] Δ is the cumulative displacement of the strain rod 4 on the horizontal plane (m).

[0115] The strain bar 4 bends under the force of the landslide, and the side in the direction of the landslide displacement is compressed and deformed, and the side in the direction of the landslide displacement is tensile. This is reflected in the displacement value fed back by the strain gauge 5. For the microstrain in the x direction, ε x+i <0,ε x-i >0, and there are several cases for the microstrain in the y direction.

[0116] When the x+ direction strain gauge 5 is consistent with the main sliding direction of the landslide, the microstrain in the y direction is ε y+i =ε y-i =0, at this time the main sliding direction is the x+ direction.

[0117] When the x+ direction strain gauge 5 is offset from the main sliding direction of the landslide, if the main sliding direction is between the x+ direction and the y+ direction, the microstrain in the y direction is ε y+i <0<ε y-i ; If the main sliding direction is between the x+ direction and the y- direction, the microstrain in the y direction is ε y-i <0<ε y+i .

[0118] S6, please refer to Figure 5 , the angle between the microstrain in the x+ direction of strain unit i and the actual main sliding direction of the landslide is set to α i (With x+ direction as the reference direction, the main sliding direction rotates clockwise as a positive value, and rotates counterclockwise as a negative value), then

[0119]

[0120] Then the degree of deviation between the actual main sliding direction of the landslide and the x+ direction can be calculated by the following formula:

[0121]

[0122] Where:

[0123] R i is the curvature radius of the strain rod 4 in the strain unit i after bending (m);

[0124] θ i is the central angle (°) corresponding to the bending section of the strain rod 4 in the strain unit i.

[0125] The intelligent strain-type drilling inclinometer in the embodiment of the present invention can also be provided with a computer, and the detection circuit is connected to the computer. The electrical signal detected by the detection circuit is input into the computer, and the computer calculates the deformation of the landslide body and displays it through a human-computer interaction interface; when the deformation value reaches the set deformation threshold, an early warning is issued.

[0126] In this document, the directional words such as front, back, top, and bottom are defined by the positions of the components in the drawings and the positions of the components relative to each other, and are only for the sake of clarity and convenience in expressing the technical solution. It should be understood that the use of the directional words should not limit the scope of protection claimed in this application.

[0127] In the absence of conflict, the above embodiments and features in the embodiments may be combined with each other.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A strain gauge drilling inclination measurement method, characterized in that: An intelligent strain-type borehole inclinometer is used, which includes an inclinometer outer tube, a plurality of force transmission sheets, a strain rod and a detection circuit. Both ends of the inclinometer outer tube are sealed, the force transmission sheets are circular, all the force transmission sheets are arranged inside the inclinometer outer tube, and the side wall of each force transmission sheet is attached to and fixedly connected with the inner wall of the inclinometer outer tube. All the force transmission sheets are spaced apart along the axial direction to separate the inclinometer outer tube into a plurality of strain units. The strain rod is arranged on the axis of the inclinometer outer tube, penetrates and is fixedly connected to all the force transmission sheets. Four resistance strain sheets are arranged in each strain unit, and the four resistance strain sheets are fixed to the outer wall of the strain rod and are evenly distributed around the outer wall of the strain rod. All the resistance strain sheets on the strain rod are arranged into four busbars of the strain rod. The detection circuit is respectively connected to the four resistance strain sheets of each strain unit. The detection circuit is used to obtain electrical signals from the four resistance strain sheets of each strain unit, and calculate the displacement corresponding to the landslide section corresponding to each strain unit according to these electrical signals. The strain gauge drilling inclination measurement method comprises the following steps: S1 predicts the main sliding direction of the landslide, and arranges the inclinometer outer tube in a borehole on the landslide so that two opposing resistance strain gauges of the strain unit are arranged along the predicted main sliding direction of the landslide; S2: the sliding of the landslide causes the inclinometer outer tube to bend, the strain rod and the inclinometer outer tube to bend synchronously, and the four resistance strain gauges in each strain unit are deformed to generate electrical signals; S3 The detection circuit calculates the microstrain of each resistive strain gauge from the relationship between resistance and strain, and numbers the strain units of the inclinometer outer tube. The strain unit at the bottom is numbered 1, and the number increases upwards. The direction of the resistive strain gauge of strain unit i along the main sliding direction is defined as the x+ direction, and the microstrain generated is ε x+i , i = 1, 2, 3, ..., the direction of the resistive strain gauge opposite to the main sliding direction is defined as the x-direction, and the microstrain generated is ε x-i , there is ε x+i +ε x-i = 0, the direction of the resistive strain gauge rotated 90° counterclockwise along the main sliding direction is defined as the y+ direction, and the microstrain generated is ε y+i , the direction of the resistive strain gauge rotated 90° clockwise along the main sliding direction is defined as the y-direction, and the microstrain generated is ε y-i , there is ε y+i +ε y-i =0; S4 calculates the displacement of each strain unit according to the geometric relationship, specifically: Horizontal displacement in x+ direction: Horizontal displacement in y+ direction: The total horizontal displacement in the x+ direction and the y+ direction is: Where: r is the cross-sectional radius of the strain bar, m; l is the original length of the strain bar of the strain unit, m; Δ xi is the horizontal displacement in the x+ direction at the upper end point of the strain bar of the strain unit, m; Δ yi is the horizontal displacement in the y+ direction at the upper end point of the strain bar of the strain unit, m; Δ i is the combined horizontal displacement in the x+ direction and the y+ direction at the upper end point of the strain rod of the strain unit, m.

2. A strain gauge drilling inclination measurement method as claimed in claim 1, characterized in that: The surface of each of the force transmission plates is provided with four reinforcing ribs distributed in a cross shape.

3. A strain gauge drilling inclination measurement method as claimed in claim 1, characterized in that: All the force transmission sheets are evenly distributed along the axial direction of the inclinometer outer tube, and the axial distance between the resistance strain sheets of two adjacent strain units is equal to the length of the strain unit.

4. A strain gauge drilling inclination measurement method as claimed in claim 1, characterized in that: Each of the strain units is 1 m in length.

5. A strain gauge drilling inclination measurement method as claimed in claim 1, characterized in that: It also includes S5, which calculates the cumulative displacement of the strain bar as follows: Cumulative horizontal displacement in the x direction: Cumulative horizontal displacement in the y direction: Cumulative total horizontal displacement Where: n is the number of strain units; Δ x is the accumulated horizontal displacement in the x direction, m; Δ y is the cumulative horizontal displacement in the y direction, m; Δ is the cumulative horizontal displacement of the strain rod on the horizontal plane, m.

6. A strain gauge drilling inclination measurement method as claimed in claim 5, characterized in that: It also includes S6, setting the angle between the microstrain in the x+ direction of strain unit i and the actual main sliding direction of the landslide to α i ,but Then the degree of deviation between the actual main sliding direction of the landslide and the x+ direction is calculated by the following formula: Where: R i is the curvature radius of the strain rod of strain unit i after bending, m; θ i is the central angle of the bending section of the strain rod of strain unit i, °; R is the radius of curvature of the strain rod after bending, m; θ is the central angle of the bending section of the strain rod, °.

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