CN106679621A - Monitoring method for differential settlement of structure section based on inclination angle measurement - Google Patents

Abstract

The invention provides a monitoring method for differential settlement of a structure section based on inclination angle measurement. A node is arranged at each corner part of the structure section, at least one node except for two end points located at the side is arranged on a curve side of the structure section, a measuring point is arranged at each corner part of the structure section, the number of the measuring points arranged at the curve side of the structure section is not less than the number of the nodes, a tilt angle sensor is arranged at each measuring point and can be used for measuring a first tilt angle and a second tilt angle, relative to two mutually perpendicular directions of a horizontal surface, at each measuring point part, and the settling volume of any point in the structure section is obtained based on a reserved inverse algorithm according to the first tilt angle and the second tilt angle measured by each measuring point, so that the monitoring method for differential settlement of the structure section based on inclination angle measurement provided by the invention not only can be used for monitoring the settling volume of any point in the structure section and has high measurement result accuracy, but also is wide in application range.

Description

Structural sections relative settlement monitoring method based on measurement of dip angle

Technical field

The invention belongs to civil engineering structure monitoring field, and in particular to a kind of structural sections relative settlement based on measurement of dip angle is supervised Survey method.

Background technology

In the construction and the monitoring of operation phase of the municipal works such as bridge and tunnel, the differential settlement of works is often Engineering staff pays close attention to the most monitoring item.The bulk settling and differential settlement of works is reasonable in design and construction quality Most intuitively react.Meanwhile, relative settlement also results in structure crack, has influence on the life-span of structure and the smooth-going of vehicle pass-through Property, it is structural health conditions and the of paramount importance index of military service performance.

The artificial measurement of the level, hydrostatic level, GPS (global positioning system) are structure sediment monitoring handss the most conventional Section, but these methods have respective limitation：Artificial measurement of the level program is complicated, is only capable of maintaining relatively low monitoring frequency, The trend that infrastructure maintenance system develops towards intelligent O＆M cannot be met；Hydrostatic level is by measuring each measuring point Liquid level or hydraulic pressure obtain the settling amount of measuring point, and the system is affected by various environmental factorss such as temperature, air pressure, pressure sensing The certainty of measurement of device limits the structure that such system monitoring has larger depth displacement with measurement range, and in addition hydrostatic level is A kind of measuring system of series connection, the damage of single measuring node will affect the precision of whole system；The precision of global positioning system Relatively low, algorithm is complicated, and insensitive for the change in measuring point short transverse.

In recent years, people have made many explorations in the structure sediment monitoring method based on inclination angle.Disclosed skill During art is converged, patent documentation CN103993530A discloses a kind of track sedimentation both sides device based on angular surveying and measurement side Method, the method arranges in orbit multiple surveys and a measurement car, uses with measuring point encoder equipped with position sensor on measurement car In guaranteeing vehicle arrival measuring point and carrying out angular surveying, by measuring the angle inverting track elevation for obtaining；Patent documentation CN104142137A discloses a kind of tunnel Longitudinal Settlement monitoring method based on wireless tilt angle sensor, and the method is in advance in tunnel Road side wall level altitude lays a pipeline, a monitoring dolly equipped with obliquity sensor is moved in pipeline, Mei Geyi Set a distance measures the inclination angle of a pipeline, so as to pass through the settling amount of the distance and inclination value inverting whole piece shield tunnel for moving. In above-mentioned both approaches, track and tunnel are regarded as into the summation of multistage broken line, and the inverting of settling amount are carried out based on the hypothesis, This can cause sizable error in the settlement monitoring of long range.Patent documentation CN104807434A discloses a kind of high-speed iron Road subgrade settlement deformation monitoring method, the method arranges a number of steel pipe in high speed railway track bearing of trend, in steel pipe Obliquity sensor is provided with, the shape of roadbed is assumed to be into a quartic polynomial, obtained by bringing measurement of dip angle value into inverse Undetermined coefficient, so as to obtain the shape of whole section of roadbed.

In above-mentioned disclosed technology, regard tunnel and roadbed as an one-dimensional linear structure, but in reality In, even tunnel and the linear facility of this kind of overlength of bridge are also to be made up of multiple structural sections, heavy in each structural sections Drop amount is independent, and single structure section will be deformed upon in the height direction in the presence of external load, heavy so as to make a difference Drop, additionally, single structure section is frequently not linear structure, its relative settlement in the direction of the width can not be ignored.

The content of the invention

The present invention is carried out to solve the above problems, it is therefore intended that providing one kind can be in monitoring of structures section arbitrarily The settling amount of point, measurement result degree of accuracy is high, and the structural sections relative settlement monitoring side based on measurement of dip angle applied widely Method.

The invention provides a kind of structural sections relative settlement monitoring method based on measurement of dip angle, it is characterised in that include Following steps：

Step 1, arranges multiple nodes in structural sections, and node setting principle is：It is all provided with each corner point of structural sections Put a node, when the side of structural sections is curve, this while at least provided with one except positioned at this while two-end-point node.

Step 2, arranges multiple measuring points in structural sections, in the position mounted angle sensor of each measuring point, for measuring All measuring points with respect to the horizontal plane go up the first inclination angle and the second inclination angle between orthogonal both direction, measuring point setting principle For：A measuring point is respectively provided with each corner point of structural sections, the quantity of measuring point is saved no less than on the side in structural sections each edge The quantity of point.

Step 3, structure is obtained according to first inclination angle and the second inclination angle of the measurement of all obliquity sensors based on pre-defined rule The sedimentation value of arbitrfary point in section.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, in step 3, the sedimentation value of arbitrfary point is obtained using inversion algorithm in structural sections, the step of inversion algorithm Suddenly include：

Step 3-1, sets up rectangular coordinate system, two coordinate axess of rectangular coordinate system respectively with the phase of obliquity sensor measurement Mutually vertical both direction is identical, and the coordinate in structural sections is (x, y), then the coordinate of node is (x_i,y_i), the coordinate of measuring point is (x_ak,y_ak), wherein i, ak are positive integer, and ak >=i；

Step 3-2, sets up natural system of coordinates, the natural system of coordinates and natural coordinates in isoparametric element in Finite Element Method It is that method for building up is identical, the structural sections is mapped as into a square shaped cells, the square under the natural system of coordinates The center of unit overlaps with described natural system of coordinates origin, and the coordinate in square shaped cells is (ζ, η), then node in structural sections Coordinate be mapped as (ζ_i,η_i), the coordinate of measuring point is mapped as (ζ_ak,η_ak), wherein i, ak are positive integer, and ak >=i；

Step 3-3, under the natural system of coordinates, sets up the shape function N corresponding with each node_i(ζ, η), the shape Function N_iThe characteristics of (ζ, η)：For the shape function at each node, the N at the node_i(ζ, η)=1, the N at other nodes_i (ζ, η)=0；

Step 3-4, the coordinate of shape function, each node according to each node obtains the rectangular coordinate system based on pre-defined rule Under coordinate (x, y) and the natural system of coordinates under coordinate (ζ, η) between mapping relations；

Step 3-5, based on pre-defined rule sedimentation value at arbitrfary point sedimentation value and each node shape function and each node is set up Function；

Step 3-6, according in the first inclination angle of the measurement of each measuring point updip angle transducer and the second inclination angle, step 3-5 The mapping between coordinate (ζ, η) under coordinate (x, y) under the function, the rectangular coordinate system that arrive and the natural system of coordinates is closed System obtains the sedimentation value at each node based on pre-defined rule；

Step 3-7, is based in step 3-5 according to the mapping relations obtained in the sedimentation value at each node, step 3-4 and obtains Function obtain the sedimentation value of arbitrfary point in structural sections.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, the mapping relations in step 3-4 are obtained by following steps：

Step 3-4a, by the abscissa of arbitrfary point in the structural sections letter of the abscissa of the shape function and each node of each node Number represents that formula is as follows：

By the abscissa of arbitrary coordinate in the structural sections function representation of the abscissa of the shape function and each node of each node, Formula is as follows：

Between coordinate (ζ, η) on coordinate (x, y) and isoparametric element under step 3-4b, rectangular coordinate system under natural system of coordinates Mapping relations it is as follows：

Wherein, x for arbitrfary point abscissa, x_iFor the abscissa of each node, By formula (1) (2) local derviation is asked to obtain the ζ and η respectively.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, in step 3-5, the function of sedimentation value at arbitrfary point sedimentation value and each node shape function and each node For：

Wherein, u (x, y) represents the sedimentation value of arbitrfary point in structural sections, u (x_i,y_i) represent the sedimentation value of each node.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, in step 3-5, the sedimentation value at each node is obtained by following steps：

Step 3-6a, by the function in step 3-5 respectively to rectangular coordinate system in two independent variables x and y ask local derviation to obtain Each point is respectively relative to the slope expression of two coordinate axess in structural sections：

Wherein, k_xFor each point in structural sections relative to x-axis slope, k_yFor each point in structural sections relative to y-axis slope, u (x, y) represents the sedimentation value of arbitrfary point in structural sections,

And then obtain the slope expression that each measuring point is respectively relative to two coordinate axess：

Step 3-6b, the first inclination angle and the second inclination angle measured by obliquity sensor obtains each measuring point difference in structural sections Relative to the slope value of two coordinate axess,

k_y=-tan φ_ak

k_x=tan θ_ak

Wherein, φ_akFor measuring point relative to y-axis direction inclination angle, θ_akFor measuring point relative to x-axis direction inclination angle, inclination angle pass The angle that sensor is measured it is positive and negative, under rectangular coordinate system with right-hand screw rule determination.

Step 3-6c, the slope value that the slope expression obtained according to step 3-6a, step 3-6b are obtained utilizes optimization Method obtains the sedimentation value of each node,

First, the slope expression both sides obtained in step 3-6a are represented in the form of matrix, then, by step The slope value that 3-6b is obtained brings above formula into, and the sedimentation value for obtaining each node using optimization method obtains each section based on pre-defined rule The sedimentation value of point.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, in step 1, the quantity of the node in the curved side of structural sections is according to the curved of the curved side of structural sections Bent pattern is arranged.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, obliquity sensor is double-shaft tilt angle sensor, the angle between two axles of double-shaft tilt angle sensor For 90 °.

Further, in the structural sections relative settlement monitoring method based on measurement of dip angle that the present invention is provided, can also have There is such feature：Wherein, obliquity sensor is inclinometer or gyroscope.Advantages of the present invention is as follows：

According to the structural sections relative settlement monitoring method based on measurement of dip angle involved in the present invention, due to by structural sections Corner is respectively provided with a node, and at least one is respectively provided with except the node positioned at the side two-end-point in the curved side of structural sections, A measuring point is respectively provided with the corner of structural sections, the quantity of the measuring point being respectively provided with the curved side of structural sections is no less than node The set-up mode of quantity, node and measuring point can according to the shape of structural sections and the sedimentation profile being likely to occur reasonable Arrangement, from And can more comprehensively reflect the stressing conditions of structural sections, and the structural sections that edge is straight line are applicable not only to, it is also applied for edge For the structural sections of curve, the scope of application is wider, and obliquity sensor is arranged at each measuring point, and obliquity sensor can measure the measuring point With respect to the horizontal plane at first inclination angle and the second inclination angle of orthogonal both direction, obliquity sensor measurement measuring point is at place Sedimentation in orthogonal both direction, the stressing conditions that can reflect in more detail at measuring point so that measurement is more accurate, The sedimentation of any point in structural sections is obtained based on predetermined inversion algorithm according to first inclination angle and the second inclination angle of each measuring point measurement Amount, therefore, the structural sections relative settlement monitoring method based on measurement of dip angle of the present invention can not only be in monitoring of structures section arbitrarily The settling amount of point, measurement result degree of accuracy is high, and applied widely.

Description of the drawings

Fig. 1 is the inserting knot figure of structural sections in embodiments of the invention；

Fig. 2 is the point layout figure of structural sections in embodiments of the invention；

Fig. 3 is the mapping of structural sections under natural system of coordinates in embodiments of the invention.

Specific embodiment

In order that technological means, creation characteristic, reached purpose and effect that the present invention is realized are easy to understand, it is real below Apply example and combine accompanying drawing and the present invention is specifically addressed based on the structural sections relative settlement monitoring method of measurement of dip angle.

In the present embodiment, comprised the following steps based on the structural sections relative settlement monitoring method of measurement of dip angle：

Step 1, according to the shape of structural sections and the sedimentation profile of prediction multiple nodes are arranged in structural sections, and node is arranged Principle is：A node is respectively provided with each corner point of structural sections, when the side of structural sections is curve, at least provided with one on the side The individual node except positioned at the side two-end-point.Wherein, curve of the quantity of the node in the curved side of structural sections according to structural sections The beam mode on side is arranged,.And 1,2 is numbered to each node ..., i ..., i are positive integer.

In the present embodiment, as shown in figure 1, it is curve that structural sections there are two sides, in the corner point of structural sections one is respectively provided with Individual node, and numbering 1,2,3,4 respectively, in the centre position of every curved side 1 node, and numbering 5,6 are respectively provided with.

Step 2, arranges multiple measuring points in structural sections, in the position mounted angle sensor of each measuring point, in this enforcement In example, obliquity sensor is double-shaft tilt angle sensor, and the angle between two axles of double-shaft tilt angle sensor is 90 °.Inclination angle passes Sensor can be inclinometer, gyroscope etc..Obliquity sensor be used for measure all measuring points with respect to the horizontal plane go up it is orthogonal The first inclination angle and the second inclination angle between both direction.In the present embodiment, orthogonal both direction is respectively structural sections Length and width both direction, therefore the first inclination angle and the second inclination angle are respectively equivalent to the point in structural sections relative to level The inclination angle of the inclination angle of face length direction, with respect to the horizontal plane width.Measuring point setting principle is：In each angle point of structural sections Place is respectively provided with a measuring point, quantity of the quantity of measuring point no less than node on the side in structural sections each edge.Wherein, the position of measuring point Putting can be completely superposed with node, it is also possible to not exclusively overlap.And 1,2 is numbered to each node ..., ak ..., ak are Positive integer.

In the present embodiment, as shown in Fig. 2 the structural sections wherein shown in Fig. 2 are identical with structural sections in Fig. 1, in structure The corner point of section is respectively provided with a measuring point, and numbering a1, a2, a3, a4 respectively, and 2 measuring points are respectively provided with every curved side, Two measuring points are located at respectively fourth class office, and numbering a5, a6, a7, a8 respectively.Obliquity sensor measures respectively phase at 8 measuring points For the first inclination angle and the second inclination angle on horizontal plane between orthogonal both direction.

Step 3, according to first inclination angle and the second inclination angle of the measurement of all obliquity sensors are obtained based on pre-defined rule The sedimentation value of arbitrfary point in structural sections.In the present embodiment, the sedimentation value of arbitrfary point is obtained using inversion algorithm in structural sections, instead Algorithm is comprised the steps of：

Step 3-1, sets up rectangular coordinate system, the phase that two coordinate axess of rectangular coordinate system are measured respectively at obliquity sensor Mutually vertical both direction is identical.In the present embodiment, x-axis is consistent with structural sections length direction, y-axis and structural sections width Unanimously.Coordinate in structural sections is (x, y), then the coordinate of node is (x_i,y_i), the coordinate of measuring point is (x_ak,y_ak), wherein i, ak It is positive integer, and ak >=i.

Step 3-2, sets up natural system of coordinates, in this patent, in natural system of coordinates and Finite Element Method in isoparametric element certainly So establishment of coordinate system method is identical.As shown in figure 3, structural sections are mapped as into the pros that length of side is 2 under natural system of coordinates Shape unit, the center of square shaped cells overlaps with natural system of coordinates origin, and the coordinate in square shaped cells is (ζ, η), then structure The coordinate of node is mapped as (ζ in section_i,η_i), the coordinate of measuring point is mapped as (ζ_ak,η_ak), wherein i, ak is positive integer, and ak >= i。

Step 3-3, under natural system of coordinates, sets up the shape function N corresponding with each node_i(ζ,η).Shape function N_i(ζ, η) the characteristics of：For the shape function at each node, the N at the node_i(ζ, η)=1, the N at other nodes_i(ζ, η)=0.

In the present embodiment, under natural system of coordinates, the shape function at each node is as follows：

Step 3-4, the coordinate of shape function, each node according to each node is obtained under ordinary coor system based on pre-defined rule The mapping relations between coordinate (ζ, η) on coordinate (x, y) and isoparametric element under natural system of coordinates, mapping relations pass through following steps Obtain：

Step 3-4a, by the abscissa of arbitrfary point in the structural sections letter of the abscissa of the shape function and each node of each node Number represents that formula is as follows：

By the abscissa of arbitrary coordinate in the structural sections function representation of the abscissa of the shape function and each node of each node, Formula is as follows：

Between coordinate (ζ, η) on coordinate (x, y) and isoparametric element under step 3-4b, rectangular coordinate system under natural system of coordinates Mapping relations it is as follows：

Wherein, x for arbitrfary point abscissa, x_iFor the abscissa of each node, By formula (1) (2) local derviation is asked to obtain the ζ and η respectively.

Step 3-5, based on pre-defined rule sedimentation value at arbitrfary point sedimentation value and each node shape function and each node is set up Function, function expression is as follows：

Wherein, u (x, y) represents the sedimentation value of arbitrfary point in structural sections, u (x_i,y_i) represent the sedimentation value of each node.

Step 3-6, according in the first inclination angle of the measurement of each measuring point updip angle transducer and the second inclination angle, step 3-5 The mapping between coordinate (ζ, η) on coordinate (x, y) and isoparametric element under the function, the rectangular coordinate system that arrive under natural system of coordinates is closed System obtains the sedimentation value at each node based on pre-defined rule.Sedimentation value at each node is obtained by following steps：

Step 3-6a, by the function in step 3-5 respectively to rectangular coordinate system in two independent variables x and y ask local derviation to obtain Each point is respectively relative to the slope expression of two coordinate axess in structural sections：

Wherein, k_xFor each point in structural sections relative to x-axis slope, k_yFor each point in structural sections relative to y-axis slope,

And then obtain the slope expression that each measuring point is respectively relative to two coordinate axess：

Wherein, k_y(ak)For ak measuring points relative to y-axis slope, k_x(ak)For ak measuring points relative to x-axis slope.

Step 3-6b, the first inclination angle and the second inclination angle measured by obliquity sensor obtains each measuring point difference in structural sections Relative to the slope value of two coordinate axess,

k_y(ak)=-tan φ_ak

k_x(ak)=tan θ_ak

Wherein, φ_akIt is ak measuring points in the inclination angle in y-axis direction, θ_akIt is ak measuring points in the inclination angle in x-axis direction, obliquity sensor The angle measured it is positive and negative, under rectangular coordinate system with right-hand screw rule determination.

Step 3-6c, the slope value that the slope expression obtained according to step 3-6a, step 3-6b are obtained utilizes optimization Method obtains the sedimentation value of each node.

The slope expression both sides obtained in step 3-6a are represented in the form of matrix, the right arrange after obtain as Following formula：

In the present embodiment,

Bring the slope value that step 3-6b is obtained into above formula, using optimization method the sedimentation value of each node is obtained

Step 3-7, is based in step 3-5 according to the mapping relations obtained in the sedimentation value at each node, step 3-4 and obtains Function obtain the sedimentation value of arbitrfary point in structural sections.

By the sedimentation value u (x at each node obtained in step 3-6_i,y_i) bring the function obtained in step 3-5 into, by x, y The mapping relations obtained according to step 3-4 be scaled ζ, η, the function obtained in step 3-5 is brought into, so as to obtain arbitrfary point Sedimentation value.

Above-mentioned embodiment is the preferred case of the present invention, is not intended to limit protection scope of the present invention.

Claims (8)

1. a kind of structural sections relative settlement monitoring method based on measurement of dip angle, it is characterised in that include：

Step 1, arranges multiple nodes in structural sections, and the node setting principle is：In each corner point of the structural sections Be respectively provided with a node, when the side of the structural sections is curve, this while at least provided with one except positioned at this while two-end-point section Point；

Step 2, arranges multiple measuring points in the structural sections, in the position mounted angle sensor of each measuring point, is used for The first inclination angle and the second inclination angle that all measuring points are with respect to the horizontal plane gone up between orthogonal both direction are measured, it is described Measuring point setting principle is：A measuring point, measuring point in the structural sections each edge are respectively provided with each corner point of the structural sections Quantity no less than node on the side quantity；

Step 3, according to first inclination angle and the second inclination angle of all obliquity sensor measurements are obtained based on pre-defined rule The sedimentation value of arbitrfary point in structural sections.

2. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 1, it is characterised in that：

Wherein, in step 3, the sedimentation value of arbitrfary point is obtained using inversion algorithm in the structural sections, is wrapped the step of inversion algorithm Contain：

Step 3-1, sets up rectangular coordinate system, and two coordinate axess of rectangular coordinate system are mutually vertical with obliquity sensor measurement respectively Straight both direction is identical, and the coordinate in structural sections is (x, y), then the coordinate of node is (x_i,y_i), the coordinate of measuring point is (x_ak, y_ak), wherein i, ak are positive integer, and ak >=i；

Step 3-2, sets up natural system of coordinates, and the natural system of coordinates is built with natural system of coordinates in isoparametric element in Finite Element Method Cube method is identical, and the structural sections are mapped as into a square shaped cells, the square shaped cells under the natural system of coordinates Center overlap with described natural system of coordinates origin, the coordinate in square shaped cells be (ζ, η), then in structural sections node seat Mark is mapped as (ζ_i,η_i), the coordinate of measuring point is mapped as (ζ_ak,η_ak), wherein i, ak are positive integer, and ak >=i；

Step 3-3, under the natural system of coordinates, sets up the shape function N corresponding with each node_i(ζ, η), the shape function N_iThe characteristics of (ζ, η)：For the shape function at each node, the N at the node_i(ζ, η)=1, the N at other nodes_i(ζ,η) =0；

Step 3-4, the coordinate of shape function, each node according to each node is obtained under the rectangular coordinate system based on pre-defined rule The mapping relations between coordinate (ζ, η) under coordinate (x, y) and the natural system of coordinates；

Step 3-5, based on pre-defined rule the function of sedimentation value at arbitrfary point sedimentation value and each node shape function and each node is set up；

Step 3-6, according to what is obtained in the first inclination angle of the measurement of each measuring point updip angle transducer and the second inclination angle, step 3-5 The mapping relations base between coordinate (ζ, η) under coordinate (x, y) under function, the rectangular coordinate system and the natural system of coordinates The sedimentation value at each node is obtained in pre-defined rule；

Step 3-7, according to the mapping relations obtained in the sedimentation value at each node, step 3-4 based on the letter obtained in step 3-5 Number obtains the sedimentation value of arbitrfary point in structural sections.

3. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 2, it is characterised in that：

Wherein, the mapping relations in step 3-4 are obtained by following steps：

Step 3-4a, by the abscissa of arbitrfary point in the structural sections function table of the abscissa of the shape function and each node of each node Show, formula is as follows：

$x=\underset{i=1}{\overset{n}{\Σ}}{N}_i(\mathrm{\ζ},\mathrm{\η})x_i---\left(1\right)$

By the abscissa of arbitrary coordinate in the structural sections function representation of the abscissa of the shape function and each node of each node, formula It is as follows：

$y=\underset{i=1}{\overset{n}{\Σ}}{N}_i(\mathrm{\ζ},\mathrm{\η})y_i---\left(2\right)$

Reflecting between the coordinate (ζ, η) on the coordinate (x, y) and isoparametric element under step 3-4b, rectangular coordinate system under natural system of coordinates Penetrate relation as follows：

$\left[\begin{array}{c}\frac{\∂N_i(\mathrm{\ζ},\mathrm{\η})}{\∂x}\\ \frac{\∂N_i(\mathrm{\ζ},\mathrm{\η})}{\∂y}\end{array}\right]=J^{-1}\left[\begin{array}{c}\frac{\∂N_i(\mathrm{\ζ},\mathrm{\η})}{\∂\mathrm{\ζ}}\\ \frac{\∂N_i(\mathrm{\ζ},\mathrm{\η})}{\∂\mathrm{\η}}\end{array}\right]---\left(3\right)$

$J=\left[\begin{array}{cc}\frac{\∂x}{\∂\mathrm{\ζ}}& \frac{\∂y}{\∂\mathrm{\ζ}}\\ \frac{\∂x}{\∂\mathrm{\η}}& \frac{\∂y}{\∂\mathrm{\η}}\end{array}\right]---\left(4\right)$

Wherein, x for arbitrfary point abscissa, x_iFor the abscissa of each node, By formula (1) (2) point It is other to ask local derviation to obtain ζ and η.

4. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 2, it is characterised in that：

Wherein, in step 3-5, the function of sedimentation value is at arbitrfary point sedimentation value and each node shape function and each node：

$u(x,y)=\underset{i=1}{\overset{n}{\Σ}}{N}_i(\mathrm{\ζ},\mathrm{\η})u(x_i,y_i)$

Wherein, u (x, y) represents the sedimentation value of arbitrfary point in structural sections, u (x_i,y_i) represent the sedimentation value of each node.

5. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 2, it is characterised in that：

Wherein, in step 3-6, the sedimentation value at each node is obtained by following steps：

Step 3-6a, by the function in step 3-5 respectively to rectangular coordinate system in two independent variables x and y ask local derviation to be tied Each point is respectively relative to the slope expression of two coordinate axess in structure section：

$k_y=\frac{\∂u(x,y)}{\∂x}$

$k_x=\frac{\∂u(x,y)}{\∂y}$

Wherein, k_xFor each point in structural sections relative to x-axis slope, k_yFor each point in structural sections relative to y-axis slope, u (x, Y) sedimentation value of arbitrfary point in structural sections is represented,

And then obtain the slope expression that each measuring point is respectively relative to two coordinate axess：

$k_y=\frac{\∂u(x_{ak},y_{ak})}{\∂x}$

$k_x=\frac{\∂u(x_{ak},y_{ak})}{\∂y}$

Step 3-6b, it is relative respectively that the first inclination angle and the second inclination angle measured by obliquity sensor obtains each measuring point in structural sections In the slope value of two coordinate axess,

k_y=-tan φ_ak

k_x=tan θ_ak

Wherein, φ_akFor measuring point relative to y-axis direction inclination angle, θ_akFor measuring point relative to x-axis direction inclination angle, obliquity sensor The angle measured it is positive and negative, under rectangular coordinate system with right-hand screw rule determination；

Step 3-6c, the slope value that the slope expression obtained according to step 3-6a, step 3-5b are obtained utilizes optimization method The sedimentation value of each node is obtained,

First, the slope expression both sides obtained in step 3-6a are represented in the form of matrix, then, by step 3-6b The slope value for obtaining brings above formula into, and the sedimentation value for obtaining each node using optimization method obtains each node based on pre-defined rule Sedimentation value.

6. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 1, it is characterised in that：

Wherein, in step 1, the bending of the quantity of the node in the curved side of the structural sections according to the curved side of the structural sections Pattern is arranged.

7. the structural sections relative settlement monitoring method based on measurement of dip angle according to claim 1, it is characterised in that：

Wherein, the obliquity sensor be double-shaft tilt angle sensor, the angle between two axles of the double-shaft tilt angle sensor For 90 °.

8. the structural sections relative settlement monitoring method method based on measurement of dip angle according to claim 7, it is characterised in that：

Wherein, the obliquity sensor is inclinometer or gyroscope.