CN104819702B - A kind of segment deformation transmits the modification method of influence on static level elevation - Google Patents
A kind of segment deformation transmits the modification method of influence on static level elevation Download PDFInfo
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Abstract
The present invention relates to the modification method that a kind of segment deformation transmits influence on static level elevation, comprise the following steps：1) data are read, turning point number and period by section of jurisdiction deformation effect in system is determined；2) judge the type of segment deformation, if section of jurisdiction is restrained, perform step 3), if section of jurisdiction rotates, perform step 4), if section of jurisdiction crack, perform step 5)；3) the convergent parameter in section of jurisdiction is determined, elevation transmission error correction value caused by the convergent deformation of section of jurisdiction is calculated；4) parameter of section of jurisdiction rotation is determined, elevation transmission error correction value caused by the rotational deformation of section of jurisdiction is calculated；5) influence of the section of jurisdiction crack to elevation transmission error estimates tunnel horizontally or vertically convergency value according to the penetration of fracture, is modified further according to the convergent error correction values computing formula in section of jurisdiction.Compared with prior art, the present invention solves segment deformation in long distance tunnel settlement monitoring engineering influences problem to the error of static liquid level.
Description
Technical Field
The invention relates to a correction technology of a hydrostatic level system, in particular to a correction method for influence of deformation of a pipe sheet on elevation transmission of a hydrostatic level.
Background
The static leveling system is suitable for measuring multi-point relative settlement as a high-precision liquid level measuring system, and has a wide application foundation in subway engineering construction and operation maintenance. The static leveling system mainly comprises a main body container, a communicating pipe, a capacitance sensor and the like and is used for measuring the vertical displacement of each measuring point. The principle is that each measuring point is connected with a reference point through a communicating pipe, according to the principle that liquid in the measuring point keeps the same horizontal plane, when the height of a measuring pier arranged on an instrument main body is changed, the liquid level of a main body container is changed, measurement data provided with an internal sensor is changed, the sensor is used for measuring the relative change of the liquid level in each measuring point container, and the relative change is transmitted to a ground test chamber for processing and feedback through a cable or a wireless signal, so that the sedimentation deformation condition of a structural body can be monitored in real time. At present, according to different acquisition principles of static level collectors, systems such as a stepping motor type static level system, a CCD static level system, a vibrating wire type static level system, a magnetostrictive displacement static level system, a GHD static level system and the like suitable for various measuring environments have been developed.
However, the application of the static leveling in the tunnel engineering still has a large space, the static leveling is used as a data acquisition means in partial tunnel engineering monitoring, but the deep analysis of data is lacked, particularly, when the long-distance static leveling monitoring is carried out, a certain number of turning points are required to be arranged according to the tunnel gradient under the limitation of the subway tunnel environment to transmit the elevation, the phenomenon that the monitoring data of two static leveling instruments arranged on the same ring piece and used for transmitting the elevation are unmatched sometimes is found in the long-term monitoring practice, the precision of the monitoring data is seriously influenced, and the current static leveling system is lacked in a precision evaluation and correction algorithm for the influence.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a correction method for the influence of segment deformation on the static leveling elevation transmission.
The purpose of the invention can be realized by the following technical scheme:
a method for correcting the influence of deformation of a pipe sheet on elevation transmission of a static leveling is characterized by comprising the following steps:
1) reading data, and determining the number of turning points and point numbers influenced by segment deformation in the system;
2) judging the type of segment deformation, if the segment is convergent, executing the step 3), if the segment is rotary, executing the step 4), and if the segment is fractured, executing the step 5);
3) determining the parameters of segment convergence, and calculating the elevation transfer error correction value caused by segment convergence deformation;
4) determining the rotation parameters of the duct piece, and calculating the elevation transfer error correction value caused by the rotation deformation of the duct piece;
5) and estimating the horizontal or vertical convergence value of the tunnel according to the depth of the crack, and correcting according to an error correction value calculation formula of the convergence of the segment.
The step 3) of calculating the elevation transfer error correction value caused by segment convergence deformation specifically comprises the following steps:
assuming that an instrument A at a turning point is arranged on the lower semicircle of the longitudinal section of the tunnel, the tunnel will be lifted up when being converged; the instrument B is arranged on the upper semicircle of the longitudinal section of the tunnel and will be settled when the tunnel converges, and then the elevation transfer error correction value delta h of the instrument A, BABIs composed of
Where Δ h is the change in elevation of instrument A due to tunnel convergence, Δ h' is the change in elevation of instrument B due to tunnel convergence, B is the semiminor axis length of the tunnel before convergence, Δ a is the tunnel semimajor axis convergence value, yBRepresents the height difference, y, of the monitoring point B from the center of the tunnel before the tunnel convergenceAAnd representing the height difference of the monitoring point A from the center of the tunnel before the tunnel convergence.
The step 4) of calculating the elevation transfer error correction value delta h caused by the rotation deformation of the segment is specifically as follows:
wherein y' is a vertical coordinate after rotation, y is a vertical coordinate before rotation, a and b are respectively a major-minor semi-axis of the space ellipse P before tunnel deformation, and alpha is a rotation angle.
The rotation angle alpha is estimated by measuring the difference between the height difference and the initial height difference between two convergence points of the same duct piece, and the estimation formula is
Wherein the height difference delta Z of two points of the same duct piece during the initial measurement0＝ΔZ10-ΔZ20The height difference between two points of the same section is delta Z (delta Z1-delta Z2) in each monitoring.
The estimation of the horizontal or vertical convergence value of the tunnel according to the crack depth is realized by table lookup.
Compared with the prior art, the elevation transfer error model based on the hydrostatic level analyzes mathematical models of various situations of segment deformation, deduces the influence of segment deformation on the elevation of a single measuring point, obtains a calculation formula of the relative elevation variation between instruments at the rotating point, and provides a correction algorithm for the hydrostatic level elevation transfer, so that the influence of segment deformation on the measuring result is weakened, the accuracy of monitoring data of the hydrostatic level system is improved, and the monitoring results of the instruments distributed on different levels are closer to the real situation. Experiments show that the relative precision of the turning point of the static leveling system influenced by the duct piece can be improved by about 5-26 percent after being corrected by the method.
Drawings
FIG. 1 is a hydrostatic level elevation transfer schematic;
FIG. 2 is a diagram of a converging geometric model of an elliptical member;
FIG. 3 is a diagram of a tunnel convergence observation model;
FIG. 4 is a diagram of a tunnel rotation observation model;
FIG. 5 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
The invention provides a correction algorithm for influence of segment deformation on hydrostatic level elevation transfer, which provides a correction formula for influence of factors such as segment convergence and rotation on elevation transfer precision according to a mathematical model of segment deformation on hydrostatic level elevation transfer on the basis of analyzing a hydrostatic level elevation transfer error propagation model, and the main flow introduction for realizing the algorithm is as follows:
1. principle of elevation transmission of hydrostatic leveling system
According to the principle of a communicating pipe, the instruments are required to be installed on the same horizontal plane when the static leveling system is installed, however, the static leveling system is limited by the complex environment in the tunnel and the slope angle of the tunnel, a certain number of turning points need to be arranged when long-distance static leveling monitoring is carried out, namely, two instruments with different elevations are installed on a pipe sheet ring with the same mileage to realize elevation transmission. When one ring pipe piece at the rotating point is regarded as a rigid body, the relative settlement of the two instruments is fixed, and the settlement of other hydrostatic level instruments relative to the reference point can be calculated through elevation transmission. However, in practice, it is found that the monitored data are not completely matched between transition points in a few periods and in partial environments, which affects the quality of elevation transmission of the hydrostatic leveling system and requires analysis of the cause of the elevation transmission according to the monitored environments.
As shown in FIG. 1, the angle formed between the slope of the subway tunnel and the horizontal plane is α degrees, so that a turning point is needed to be set for transmitting the elevation value when the instrument is erectedAssume a reference point of the hydrostatic leveling system is Z0The monitoring points are numbered sequentially as A1、A2、A3、…、Ak1、B1、B2、B3、…、Bk2、…、N1、N2、N3、…、NknThere are (k1+ k2+ k3+ … + kn) monitor points and (N-1) transition points. Defining a reference point Z0The primary monitoring data is Z00Monitoring point NiThe primary monitoring data is Ni0Then after jth monitoring datum point Z0And monitoring point NiThe settling amount relative to the self-installation position is respectively
Settlement amount of each monitoring point relative to self installation position according to formula (1)Can calculate the relative reference point Z of each monitoring point0Amount of sedimentation ofAre respectively as
Wherein E represents a unit matrix,representing a matrix of observations except for turning points. When only elevation transfer errors are considered, assume transition point B1、C1、…、N1Respectively, areMonitor point N obtainable by covariance propagation theoremiHas a variance of
As can be seen from equation (3), the more the transition points are, the larger the elevation transmission error at the transition point is, the larger the influence on the observation result is.
2. Correction algorithm for segment convergence
The elevation transfer error caused by the convergence deformation of the duct piece is calculated after the elevation correction values of two instruments at the turning point are obtained, and the calculation process is as follows:
when the tunnel convergence is large, the relative height difference relation of different positions of the side wall of the duct piece is changed, and the larger the convergence is, the larger the influence on the structure height difference is, and the larger the error of elevation transmission is.
Assuming that the major and minor axes of the space ellipse P in which a certain ring pipe piece is located before the tunnel convergence deformation are a and b, the major and minor axes of the space ellipse Q in which the ring pipe piece is located after the convergence deformation are respectively a
a”＝a+Δa。 (4)
b”＝b+Δb
When the tunnel is converged and deformed, assuming that the tunnel perimeter L is constant, the tunnel perimeter L is changed
L＝2πb+4(a-b)＝2πb”+4(a”-b”)。 (5)
Substituting formula (4) into formula (5) to obtain:
as can be seen from the formula (6): when the tunnel is converged and deformed, the long half shaft becomes long and the short half shaft becomes short; the longer half axis becomes shorter and the shorter half axis becomes longer, and the convergence values Δ a and Δ b of the two values are in a certain proportional relationship.
In order to explore the law of elevation change of any point on the tunnel caused by convergence deformation of the segments, a geometric model of the convergence of the elliptical member shown in fig. 3 is established.
An elliptical coordinate system qOp is defined with an origin O as the center of the ellipse, Op as the major semi-axis direction, and Oq as the minor semi-axis direction, the Oq direction being in a direction that is 90 ° clockwise from Op.
The equations of the tunnel section P before convergence and the tunnel section Q after convergence in the qOp coordinate system are respectively
Wherein,elliptical coordinates of ellipses P and Q, respectively;
the long half shaft and the short half shaft of the ellipses P and Q respectively form a matrix.
Then the coordinate of any point (x, y) on the ellipse P after the tunnel convergence on the ellipse Q is (x ", y"), and the resulting elevation change value is (x, y)
Δh＝y"-y。 (8)
Assuming that there is a middle position ellipse P' in the convergence process, its major semi-axis is a and its minor semi-axis is b ", its equation is defined as
As can be seen from the geometric characteristics of the ellipse, when the ellipse P converges on the ellipse P ', the point a (x, y) moves to a' (x ', y'), and when the ellipse P 'converges on Q, the point a' (x ', y') moves to a "point (x", y "), and x ═ Δ x ″, y ═ y + Δ y. In the formula (9)By bringing the formulae (7) and (9) into the formula (8)
Equation (10) represents an estimation formula of the variation of the height difference of the single monitoring point due to the convergence of the tunnel, wherein b represents the semiminor axis length of the tunnel before convergence, Δ a represents the convergence value of the semimajor axis of the tunnel, and y represents the height difference of the monitoring point from the center of the tunnel before the convergence of the tunnel. As can be seen from equation (10), the relative elevation change of the instrument due to the convergence of the tunnel is not only related to the convergence value of the tunnel, but also related to the installation height and position of the instrument.
To discuss the extreme cases of the effect of tunnel convergence on the static level observation, an observation model as shown in fig. 4 was established.
Assuming that an instrument A at a turning point is arranged on the lower semicircle of the longitudinal section of the tunnel, the tunnel will be lifted up when being converged; the instrument B is arranged on the upper semicircle of the longitudinal section of the tunnel, and can be settled when the tunnel is converged. The relative head variation estimate of instrument A, B is formulated as
And (3) calculating an elevation transfer error correction value according to the horizontal or vertical convergence value of the duct piece and the formula (11) by using the elevation transfer error caused by the convergence deformation of the duct piece. In actual engineering, although the height difference between the monitoring point and the center of the tunnel cannot be directly measured, the height difference between the monitoring point and the center of the tunnel can be calculated according to the height difference between the monitoring point and the track surface and design parameters of the tunnel.
3. Correction algorithm for segment rotation
When the subway tunnel is in soft soil layer, or because the circumstances such as slip casting production self rotation can make the tunnel section of jurisdiction rotatory deformation, can lead to the relative position relation of static level turning point to produce the change.
A tunnel rotation observation model as shown in fig. 4 is established. Defining the rotation angle of the tunnel P as alpha, and the equation of the tunnel section P before rotation and the tunnel section Q after rotation in an elliptic coordinate system as
Wherein:elliptical coordinates representing ellipses P and Q, respectively;
a matrix of major and minor semi-axes representing ellipses P and Q.
Measuring coordinate X and elliptical coordinate XPHas a conversion relation of
XP＝X0+R(β)X。 (13)
Wherein: x0＝[x0y0]TThe amount of translation is indicated and,a rotation matrix is represented.
In order to find out the influence of tunnel rotation on the elevation value of any point on the tunnel, the rotation angle of the tunnel is converted into the rotation angle of a measurement coordinate system. Assuming that the tunnel is rotated without translation and scale transformation, the conversion relation between the measurement coordinate system X' after rotation and the measurement coordinate system X before rotation is
X'＝R(α)X。 (14)
Wherein:a rotation matrix is represented.
Then the coordinates of any point (x, y) on the ellipse P after the tunnel rotation on the ellipse Q are (x ", y"), and the resulting coordinate change value is (x ", y ″)
As can be seen from equation (15), the relative elevation change of the instrument caused by the rotation of the tunnel is related to the rotation angle of the tunnel and the installation height and position of the instrument. In engineering application, the tunnel rotation angle cannot be directly measured, and the estimation value of the rotation angle can be calculated by measuring the height difference between two convergence points of the same duct piece and the initial height difference value. Assuming that the height difference between two points of the same duct piece is delta Z in the initial measurement0＝ΔZ10-ΔZ20When the height difference between two points on the same cross section is delta Z-delta Z1-delta Z2 in each monitoring, the estimated formula of the rotation angle is
And calculating an approximate rotation angle according to an equation (16) and then driving the approximate rotation angle into an equation (15) to obtain an elevation transfer error correction value.
4. Segment crack correction algorithm
The structure and the stress characteristic of the duct piece can be influenced by the change of the cracking depth of the tunnel duct piece, so that the settlement values of different positions on the cracked duct piece are different. Under the condition that the shield segment has cracks, the maximum stress value, the horizontal and vertical convergence values and the vertical settlement values of the segment can be increased along with the reduction of the soil pressure coefficient and the foundation spring coefficient, and are increased along with the increase of the underground water level burial depth. Therefore, when static leveling turning points are arranged on the duct piece with cracks, uneven deformation of the duct piece can be caused by the cracks, and the elevation transfer error is increased.
Setting experiment parameters according to concrete structure design specifications, establishing an analysis model by adopting a three-dimensional Goodman unit method, arranging 2 groups of cracks with different depths, namely 0.45mm in width and 120 mm and 300mm in depth, on a left side segment of an experiment segment ring, arranging 4 groups of different depth simulation experiments, namely 60, 150, 240 and 300mm in depth, on a capping segment, and setting the width of the cracks to be 0.53 mm. The results of the influence of the segment crack depth on the shield segment convergence are shown in table 1.
TABLE 1 influence of crack depth on shield segment convergence mm
As can be seen from Table 1, when the cracks are located at the top and bottom of the segment, the convergence and deformation of the segment are the most serious, and along with the increase of the depth of the cracks, the horizontal convergence and the vertical convergence of the segment are slightly increased, but the amplitude is not large. When the crack depth is between 60mm and 300mm, the horizontal convergence value of the shield segment is between 3.80mm and 4.03mm, and the top-bottom vertical convergence value is between 5.13mm and 6.02 mm.
The influence of the segment cracks on the elevation transfer error is estimated according to the crack depth in the table 1 to obtain a horizontal or vertical convergence value of the tunnel, and then correction is performed according to an error correction formula (11) of segment convergence.
The basic flow of the correction algorithm for the influence of the segment deformation on the height transmission of the static leveling is as follows:
(1) and (3) calculating an elevation transfer error correction value according to the horizontal or vertical convergence value of the duct piece and the formula (11) by using the elevation transfer error caused by the convergence deformation of the duct piece. In actual engineering, although the height difference between the monitoring point and the center of the tunnel cannot be directly measured, the height difference between the monitoring point and the center of the tunnel can be calculated according to the height difference between the monitoring point and the track surface and design parameters of the tunnel.
(2) The influence of the segment cracks on the elevation transfer error can be used for estimating the horizontal or vertical convergence value of the tunnel according to the crack depth, and then the elevation transfer accuracy is improved according to an error correction formula of segment convergence.
(3) The elevation transfer error caused by the rotation deformation of the duct piece can be corrected by calculating an approximate rotation angle according to a formula (16) and then driving the approximate rotation angle into a formula (15).
Fig. 5 shows a flow chart of the algorithm of the present invention. The steps in the figures are described in detail below:
in step 401, the data of the measurement point set is read, and the point number of the transfer point in the data is determined according to the number and the position of the transfer points in the engineering project.
In step 402, one or more types of the item affected by the deformation of the segment are selected, and then step 403 is performed;
in step 403, for different segment deformation types, determining the parameter values of segment deformation according to the parameter types in the formula (11), the formula (15) and the formula (16), and then executing step 404;
in step 404, calculating a relative elevation error of a turning point according to an influence formula of segment convergence and segment rotation, correcting the read point position data, and then executing step 405;
in step 405, the relative accuracy of each point after correction is calculated and the corrected data is stored in the database, and then the algorithm is ended.
Claims (3)
1. A method for correcting the influence of deformation of a pipe sheet on elevation transmission of a static leveling is characterized by comprising the following steps:
1) reading data, and determining the number of turning points and point numbers influenced by segment deformation in the system;
2) judging the type of segment deformation, if the segment is convergent, executing the step 3), if the segment is rotary, executing the step 4), and if the segment is fractured, executing the step 5);
3) determining the parameters of segment convergence, and calculating the elevation transfer error correction value caused by segment convergence deformation;
4) determining the rotation parameters of the duct piece, and calculating the elevation transfer error correction value caused by the rotation deformation of the duct piece;
5) estimating a horizontal or vertical convergence value of the tunnel according to the depth of the crack, and correcting according to an error correction value calculation formula of the convergence of the segment;
the step 3) of calculating the elevation transfer error correction value caused by segment convergence deformation specifically comprises the following steps:
assuming that an instrument A at a turning point is arranged on the lower semicircle of the longitudinal section of the tunnel, the tunnel will be lifted up when being converged; the instrument B is arranged on the upper semicircle of the longitudinal section of the tunnel and will be settled when the tunnel converges, and then the elevation transfer error correction value delta h of the instrument A, BABIs composed of
Where Δ h is the change in elevation of instrument A due to tunnel convergence, Δ h' is the change in elevation of instrument B due to tunnel convergence, B1 represents the semi-minor length of the tunnel before convergence, Δ a represents the value of the tunnel semi-major convergence, yBRepresents the height difference, y, of the monitoring point B from the center of the tunnel before the tunnel convergenceARepresenting the height difference of a monitoring point A from the center of the tunnel before the tunnel convergence;
the step 4) of calculating the elevation transfer error correction value delta h caused by the rotation deformation of the segment is specifically as follows:
wherein y' is a vertical coordinate after rotation, y is a vertical coordinate before rotation, a and b2 are respectively a major-minor semi-axis of the space ellipse P before tunnel deformation, and alpha is a rotation angle.
2. The method of claim 1, wherein the rotation angle α is estimated by measuring the difference between the height difference between two convergence points of the same segment and the initial height difference, and the estimation formula is as follows
Wherein the height difference delta Z of two points of the same duct piece during the initial measurement0The height difference between two points on the same section is delta Z during each monitoring.
3. A method of correcting for the effect of tube sheet deformation on elevation transmission of hydrostatic level according to claim 1, wherein the estimation of the horizontal or vertical convergence of the tunnel from the depth of the fracture is performed by a table lookup.
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| CN202350780U (en) * | 2011-06-13 | 2012-07-25 | 绵阳市奇石缘科技有限公司 | Highly-intelligent settlement observation system based on principle of communicating vessels |
| US9183739B2 (en) * | 2012-06-28 | 2015-11-10 | National Applied Research Laboratories | Bridge safety monitoring integrated system with full optical fiber and the method for sensing thereof |
| CN102927966B (en) * | 2012-10-31 | 2014-11-05 | 清华大学 | Method for improving monitoring accuracy of structural settlement |
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| CN108519073B (en) * | 2018-04-12 | 2021-01-15 | 北京市市政工程研究院 | Method for judging deformation of operation subway tunnel by adopting static level |
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