A mountainous bridge tower pier close-range large-inclination verticality intersection measurement method

Abstract

This invention belongs to the field of bridge construction surveying technology, specifically a method for measuring the verticality of bridge tower piers at close range and with large inclination angles in mountainous areas. The method includes: S1, calculating the angle between the intersection hypotenuse and the vertical line of the tower pier based on the known elevation and measured slope distance of the measuring point at the top of the tower pier, then calculating the horizontal distance and solving for the first corrected coordinates of each measuring point, thus avoiding vertical angle observation errors under large inclination angles; S2, accurately measuring the actual distance between the measuring points of the two tower piers, and using this as a constraint to adjust the first corrected coordinates to obtain a high-precision second corrected coordinate for the center of the tower top; S3, calculating the verticality based on the second corrected coordinates of the tower top and the known coordinates of the tower bottom. This invention effectively overcomes the problem of low measurement accuracy caused by close-range, large-inclination angle observations in narrow mountainous terrain, eliminates the need for multi-layered control networks, improves measurement efficiency and accuracy, and reduces operational risks and costs.

Description

Technical Field

[0001] This invention relates to the field of bridge construction surveying technology, and in particular to a method for measuring the perpendicularity of bridge tower piers at close range with large inclination angles in mountainous areas. Background Technology

[0002] Bridge piers are key load-bearing structures for long-span cable-stayed bridges and suspension bridges, and their verticality during construction directly affects the structural safety and alignment of the bridge. When constructing ultra-high bridge piers in deep mountain valleys, the steep and narrow terrain limits the location of construction control points, which are often very close to the piers and located below their sides.

[0003] Traditional methods of verticality measurement face severe challenges: (1) When using a ground total station for polar coordinate measurement or a tower top total station for side intersection measurement, the angle (vertical angle) between the observation line and the plumb line is extremely large. The axis system errors of the total station (such as vertical circle index error and horizontal axis error) are significantly amplified when observing at large inclination angles, resulting in huge errors in the vertical angle observation values. When using this vertical angle to convert the tilt distance to the horizontal distance, a non-negligible conversion error will occur, which seriously reduces the measurement accuracy of the tower top plane coordinates and thus affects the reliability of the verticality calculation results. (2) In order to improve measurement conditions, sometimes multiple control networks are set up at different heights along the hillside. This is not only costly and labor-intensive, but also has the problem of systematic error transmission between control networks. Surveyors need to climb the mountain frequently, which is inefficient and has high safety risks.

[0004] Therefore, there is an urgent need for a method that can overcome the limitations of close-range and large-angle observation conditions and achieve high-precision and high-efficiency verticality measurement of bridge tower piers in mountainous areas. Summary of the Invention

[0005] This invention proposes a method for measuring the verticality of bridge piers at close range with large inclination angles in mountainous areas. It aims to solve the technical problems of low accuracy, high network setup cost, and low operation efficiency caused by large inclination angle observation when measuring the verticality of bridge piers in narrow mountainous environments.

[0006] In a first aspect, embodiments of the present invention provide a method for measuring the perpendicularity of bridge tower piers at close range with large inclination angles in mountainous areas, comprising the following steps: S1, based on the known elevation of the verticality measuring points at the top of the two tower piers, obtain the angles between the at least three intersecting hypotenuses of each tower pier and the corresponding vertical line of the tower pier, and calculate the first corrected coordinates of the verticality measuring points of each tower pier based on the angles. S2, Measure the actual distance between the two tower verticality measuring points, and use the actual distance as a constraint condition to perform constraint adjustment on the first correction coordinates of the two tower verticality measuring points to obtain their respective adjustment coordinates. Take the average of the two adjustment coordinates as the second correction coordinate of the center of the top surface of the bridge tower pier. S3. Calculate the verticality of the bridge tower pier based on the second corrected coordinates of the center of the top surface of the bridge tower pier and the known coordinates of the center of the bottom surface of the bridge tower pier.

[0007] The technical advantage of this invention's method for measuring the verticality of bridge tower piers at close range and large inclination angles is that it utilizes known elevations and measured slope distances to calculate the angle between the intersection hypotenuse and the plumb line, replacing direct observation of the vertical angle. This method fundamentally avoids the problem of total station axis system errors being amplified during large inclination angle observations, significantly reduces the error in converting slope distance to horizontal distance, and thus greatly improves the accuracy of the initial coordinates (first corrected coordinates) of the tower top measuring point. Furthermore, by introducing precise on-site measured distances between the two tower limbs as constraints for adjustment, the accumulation of instrument system errors and random errors is effectively suppressed, ultimately obtaining high-precision tower top center coordinates (second corrected coordinates), ensuring the reliability of the verticality measurement results.

[0008] Further, in S1, the angles between at least three intersecting hypotenuses of each tower leg and their corresponding vertical lines are obtained, and the first corrected coordinates of the verticality measuring points of each tower leg are calculated based on the angles, specifically including: S11. Place two total stations on the verticality measuring points at the top of the two tower limbs respectively, and measure the instrument height; measure the length of the intersection hypotenuse from the center of each total station to at least three known control points on the ground; calculate the angle between each intersection hypotenuse and the corresponding tower limb plumb line based on the known elevation of the measuring points at the top of the tower limbs, the instrument height of the total station, and the measured length of the intersection hypotenuse. S12, Calculate the horizontal projection length of each intersection hypotenuse based on the included angle and the side length of each intersection hypotenuse obtained in step S11. S13. Using the horizontal projection side length of each intersection hypotenuse and the plane coordinates of the known control points, and based on the principle of side intersection, calculate the plane coordinates of the center of the total station at the top of the two tower limbs respectively, which are used as the first corrected coordinates of the corresponding tower limb verticality measuring points.

[0009] Furthermore, in S11, the formula for calculating the included angle α is as follows: ; Wherein, ΔH is the elevation difference between the center of the total station and the ground control point, and S is the measured length of the intersection hypotenuse; the elevation difference ΔH is calculated from the known elevation of the measuring point at the top of the tower, the instrument height, and the known elevation of the ground control point.

[0010] Furthermore, the formula for calculating the horizontal projected side length D in S12 is as follows: ; Where S is the length of the intersection hypotenuse, and α is the angle between the intersection hypotenuse and the vertical line of the corresponding tower leg.

[0011] Furthermore, in S2, using the actual distance as a constraint, the first corrected coordinates of the two tower verticality measurement points are adjusted under constraint, specifically including: S21, accurately measure the actual horizontal distance between the two tower leg verticality measuring points on the ground; S22, Calculate the observation distance and observation azimuth between the two tower limb verticality measuring points based on the first corrected coordinates of the two points; S23, Calculate the deviation between the observed distance and the actual distance; S24. Using the actual distance as a strong constraint, construct an adjustment model and calculate the adjustment corrections for the two first correction coordinates. Add the first correction coordinates to the corresponding adjustment corrections to obtain the adjusted coordinates of the two measuring points.

[0012] Furthermore, the adjustment model in S24 is as follows: taking the first corrected coordinate of one measuring point as a fixed point and the observation azimuth between two measuring points as a fixed direction, the observation distance is scaled to the actual distance to obtain the adjustment coordinates of the other measuring point.

[0013] Furthermore, the adjustment model in S24 is an indirect adjustment model that uses the first corrected coordinates of the two measurement points as approximations and the distance between them equal to the actual distance as a constraint.

[0014] Furthermore, the calculation of the verticality of the bridge tower piers in S3 specifically includes: S31, calculate the difference in planar position between the second corrected coordinate of the center of the top surface of the bridge tower pier and the known coordinate of the center of the bottom surface, and obtain the tower top offset value; S32, divide the tower top offset value by the height of the bridge tower pier to obtain the verticality of the bridge tower pier.

[0015] Furthermore, the known control points are located on hillsides or stable ground near the bridge tower pier foundation.

[0016] Furthermore, the total station, mounted on the tops of the two towers, selects the same or different groups of known control points for intersection measurement based on the line-of-sight conditions. Attached Figure Description

[0017] Figure 1 This is a schematic diagram illustrating the principle of a method for measuring the verticality of bridge tower piers at close range with large inclination angles, provided in an embodiment of the present invention. Detailed Implementation

[0018] To enable those skilled in the art to better understand the technical solutions of the present invention, exemplary embodiments of the present invention are described below in conjunction with the accompanying drawings, including various details of the embodiments of the present invention to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0019] When using a ground total station for polar coordinate measurement or a tower-top total station for intersecting measurements, the angle (vertical angle) between the observation line of sight and the plumb line is extremely large. The axis system errors of the total station (such as vertical circle index error and horizontal axis error) are significantly amplified during large-angle observations, resulting in huge errors in the vertical angle observation values. When using this vertical angle to convert the tilt distance to a horizontal distance, a non-negligible conversion error occurs, severely reducing the measurement accuracy of the tower-top plane coordinates and consequently affecting the reliability of the verticality calculation results. Therefore, this invention provides a method for close-range, large-angle verticality intersection measurement of bridge tower piers in mountainous areas. This method relies entirely on ground control points located in relatively easily accessible areas such as near the pier cap, eliminating the need for multi-layered, high-density construction control networks along steep slopes, greatly reducing the cost and maintenance workload of control network deployment. Surveyors do not need to frequently climb to control points at different heights, mainly working near the top of the bridge tower pier and known ground points, significantly improving measurement efficiency and reducing safety risks.

[0020] This invention is applied to the verticality measurement of bridge pier 1 in mountainous areas. Bridge pier 1 typically consists of two tower legs 2. Known control points (such as DQ1, DQ2, DQ3) are set up in stable locations with good visibility. A total station 3 is set up at verticality measuring points B1 and B2 on the tops of the two tower legs 2. The intersection hypotenuse 4 refers to the spatial slope distance from the center of the total station to the ground control point. The tower leg plumb line 5 is a straight line passing through the measuring points on the tower leg and perpendicular to the horizontal plane.

[0021] refer to Figure 1 Specifically, it includes the following steps: S1: Obtain the first corrected coordinates of the two tower limb verticality measurement points B1 and B2. The core of this step is to use geometric relationships to calculate the included angle using known elevations and slope distances, replacing the error-prone vertical angle observation. Specifically, this includes the following steps: S11: Angle Calculation. Place the total station I at measuring point B1 on the top of tower leg 2, center and level it, and measure the instrument height h. I (That is, the vertical height from point B1 to the center of the horizontal axis of the total station). Similarly, place the total station II at measuring point B2 and measure the instrument height h. IIThe elevations of measuring points B1 and B2 are known to be HB1 and HB2 respectively (which can be determined in advance through precise leveling or trigonometric leveling). Then the elevations of the horizontal axis centers of the two total stations are: ; ; Measure the slope distance S to at least three known control points on the ground (e.g., DQj, j=1,2,3...) using total station I and total station II respectively. Ij and S IIj The elevation of control point DQj is known to be H. Dj The plane coordinates are (X Dj ,Y Dj ).

[0022] The angle α between the hypotenuse of the intersection point I of the total station and the control point DQj and the vertical line of the tower leg B1 is... j It can be calculated using the following formula: ; In the formula, ΔH Ij Let be the elevation difference between the center of total station I and control point DQj. Similarly, the included angle β corresponding to total station II can be calculated. j .

[0023] This calculation process does not involve total station observations of vertical angles; it only utilizes the elevation difference (obtained from known elevations and instrument height) and the measured slope distance, thus completely avoiding the influence of vertical circle axis errors. It should be noted that the number of known ground control points should not be less than three, and the intersection diagram formed with the tower top measuring point should be as good as possible (e.g., not a narrow, elongated triangle) to improve the strength and accuracy of the intersection solution. Two total stations can select the same or different sets of ground control points for intersection based on line-of-sight, offering high flexibility.

[0024] S12: Calculate the horizontal side length. Use the included angle α obtained in step S11. j β j and measured slope distance S Ij S IIj Calculate the horizontal projection side length D of each intersection hypotenuse. Ij D IIj : ; .

[0025] S13: Coordinate Calculation. For total station I, the horizontal distances D from it to multiple control points DQj are known. Ij and the precise planar coordinates (X) of each control point Dj ,Y DjThis constitutes a distance intersection problem. The most probable plane coordinates of the total station I center (i.e., measuring point B1) can be obtained by establishing a distance equation and performing adjustment using the least squares method. This is the first corrected coordinate of point B1. Similarly, the first corrected coordinate of point B2 can be calculated. .

[0026] The "equivalent vertical angle" used for slope distance reduction is obtained indirectly through mathematical calculation, which eliminates the adverse effects of systematic errors such as instrument vertical axis tilt and vertical circle index difference under large tilt angles, significantly improves the accuracy of the initial coordinate solution, and lays a reliable foundation for subsequent steps.

[0027] S2: Constrained adjustment is performed using the actual distance between the two measuring points to obtain the second corrected coordinates of the center of the bridge pier top surface. The coordinates are further optimized using the inherently stable geometric constraints of the bridge pier (distance between the two tower limbs). Specifically, the following steps are included: S21: Distance Measurement. At the top of the bridge tower pier, using a calibrated steel tape or a high-precision total station, accurately measure the actual horizontal distance S between the two tower top verticality measuring points B1 and B2. true This distance is a structural dimension of the bridge pier itself, and it is highly accurate and stable.

[0028] S22: Observation Calculation. Based on the first corrected coordinates obtained in step S13, calculate the observation distance S between points B1 and B2. obs and the observed azimuth angle θ obs : ; ; This model forces the distance between two points to conform to the true value while maintaining the relative orientation of the observations. A more rigorous adjustment can treat the coordinates of both B1 and B2 as parameters, perform an overall adjustment with distance as a constraint, and solve for the coordinate corrections.

[0029] Finally, the adjusted coordinates of point B1 In the simplified model, this is... During the overall adjustment, the B1 coordinates will also receive a slight correction. These coordinates are the adjusted coordinates of the two tower leg verticality measurement points.

[0030] S25: Center determined. Coordinates (X, Y, F) of the center O of the top surface of the bridge tower pier. O ,Y O The average of the adjusted coordinates of the two tower limb measuring points is obtained: ; ; This coordinate is the second corrected coordinate of the center of the top surface of the bridge tower pier, and its accuracy is better than that of the first corrected coordinate.

[0031] By using the precise geometric dimensions of the bridge pier itself as a strong constraint, the initial coordinates can be calibrated and optimized. This can effectively absorb and reduce the systematic deviations (such as constant errors) that may exist when the two instruments measure independently, as well as the errors caused by different control point groups, making the final tower top center coordinates more reliable.

[0032] S3: Calculate the verticality of the bridge tower piers based on the second corrected coordinates of the tower top center and the known coordinates of the tower base center A. Specifically, this includes: S31: Offset value calculation. The design coordinates of the center A of the bridge pier base, or the known coordinates determined through precision measurement, are (X...). A ,Y A ). Calculate the planar offset (ΔX, ΔY) of the top surface center O relative to the bottom surface center A, and the total offset value δ: ; ; .

[0033] S32: Verticality Calculation. Given the design height H of the bridge tower pier (or the height difference between points A and O), the verticality τ of the bridge tower pier is: ; It is usually expressed as a ratio (such as 1 / H) or a percentage.

[0034] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A method for measuring the perpendicularity of bridge tower piers at close range with large inclination angles in mountainous areas, characterized in that, Includes the following steps: S1, based on the known elevation of the verticality measuring points at the top of the two tower piers, obtain the angles between the at least three intersecting hypotenuses of each tower pier and the corresponding vertical line of the tower pier, and calculate the first corrected coordinates of the verticality measuring points of each tower pier based on the angles. S2, Measure the actual distance between the two tower verticality measuring points, and use the actual distance as a constraint condition to perform constraint adjustment on the first correction coordinates of the two tower verticality measuring points to obtain their respective adjustment coordinates. Take the average of the two adjustment coordinates as the second correction coordinate of the center of the top surface of the bridge tower pier. S3. Calculate the verticality of the bridge tower pier based on the second corrected coordinates of the center of the top surface of the bridge tower pier and the known coordinates of the center of the bottom surface of the bridge tower pier.

2. The method according to claim 1, characterized in that, In step S1, the angles between at least three intersecting hypotenuses of each tower segment and their corresponding vertical lines are obtained. Based on these angles, the first corrected coordinates of the verticality measuring points of each tower segment are calculated, specifically including: S11. Place two total stations on the verticality measuring points at the top of the two tower limbs respectively, and measure the instrument height; measure the length of the intersection hypotenuse from the center of each total station to at least three known control points on the ground; calculate the angle between each intersection hypotenuse and the corresponding tower limb plumb line based on the known elevation of the measuring points at the top of the tower limbs, the instrument height of the total station, and the measured length of the intersection hypotenuse. S12, Calculate the horizontal projection length of each intersection hypotenuse based on the included angle and the side length of each intersection hypotenuse obtained in step S11. S13. Using the horizontal projection side length of each intersection hypotenuse and the plane coordinates of the known control points, and based on the principle of side intersection, calculate the plane coordinates of the center of the total station at the top of the two tower limbs respectively, which are used as the first corrected coordinates of the corresponding tower limb verticality measuring points.

3. The method according to claim 2, characterized in that, In S11, the formula for calculating the included angle α is as follows: ； Wherein, ΔH is the elevation difference between the center of the total station and the ground control point, and S is the measured length of the intersection hypotenuse; the elevation difference ΔH is calculated from the known elevation of the measuring point at the top of the tower, the instrument height, and the known elevation of the ground control point.

4. The method according to claim 2, characterized in that, The formula for calculating the horizontal projected side length D in S12 is as follows: ； Where S is the length of the intersection hypotenuse, and α is the angle between the intersection hypotenuse and the vertical line of the corresponding tower leg.

5. The method according to claim 1, characterized in that, In S2, using the actual distance as a constraint, the first corrected coordinates of the two tower verticality measuring points are adjusted under constraint, specifically including: S21, accurately measure the actual horizontal distance between the two tower leg verticality measuring points on the ground; S22, Calculate the observation distance and observation azimuth between the two tower limb verticality measuring points based on the first corrected coordinates of the two points; S23, Calculate the deviation between the observed distance and the actual distance; S24. Using the actual distance as a strong constraint, construct an adjustment model and calculate the adjustment corrections for the two first correction coordinates. Add the first correction coordinates to the corresponding adjustment corrections to obtain the adjusted coordinates of the two measuring points.

6. The method according to claim 5, characterized in that, The adjustment model in S24 is as follows: taking the first corrected coordinate of one measuring point as a fixed point and the observation azimuth between two measuring points as a fixed direction, the observation distance is scaled to the actual distance to obtain the adjustment coordinates of the other measuring point.

7. The method according to claim 5, characterized in that, The adjustment model described in S24 is an indirect adjustment model that uses the first corrected coordinates of two measurement points as approximations and the distance between them equal to the actual distance as a constraint.

8. The method according to claim 1, characterized in that, The calculation of the verticality of the bridge tower piers in S3 specifically includes: S31, calculate the difference in planar position between the second corrected coordinate of the center of the top surface of the bridge tower pier and the known coordinate of the center of the bottom surface, and obtain the tower top offset value; S32, divide the tower top offset value by the height of the bridge tower pier to obtain the verticality of the bridge tower pier.

9. The method according to claim 2, characterized in that, The known control points are located on hillsides or stable ground near the bridge tower pier foundation.

10. The method according to claim 2, characterized in that, The total station, mounted on the tops of the two towers, selects the same or different groups of known control points for intersection measurement based on the line-of-sight conditions.

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