CN101685012A - Measuring and calculating method of subway tunnel section - Google Patents

Abstract

The invention discloses a measuring and calculating method of a subway tunnel section, comprising the following steps: 1) calculating the coordinates of the tunnel line center, and lofting in the tunnel; 2) installing a prism-free total station on the central line of the tunnel; 3) back viewing by a known point, measuring altitude difference, calculating the elevation of sight of the total stationand inputting into the prism-free total station; 4) collecting an observation point coordinates on a cross-section circle, and storing the coordinates into the total station; 5) rotating the prism-free total station for180 degrees along the cross shaft, and collecting and storing the observation point coordinates on the cross-section circle again; 6) performing cross section model fitting according to the collected data; 7) calculating the center and the radius of the fitting circle; and 8) calculating the needed elevation and chord length according to the center and the radius of the circle.The invention fits the collected data by inputting into the section model, a calculation value and a practical measuring data have small error, thus the method of the invention can be applied in practical work. In addition, the invention has the advantages of simple operation and convenient use, greatly saves field operating time and improves working efficiency.

Description

The measurement of subway tunnel section and computing method

Technical field

The present invention relates to a kind of Tunnel transverse section measuring technology, be used in particular for the section survey method in shield construction tunnel.The main method that adopts the non-prism total powerstation to carry out tunnel cross-section measurement.

Background technology

In order to guarantee mating formation smoothly of underground railway track, after shield tunnel construction is finished, generally to carry out the measurement of holing-through survey and tunnel cross section.Tunnel holing through is measured conventional tracerse survey and the measurement of the level of general employing and can be solved, and tunnel cross section is measured the general method of profiler or total powerstation cooperation laser transit that adopts and carried out.

Summary of the invention

The objective of the invention is measurement and computing method by a kind of subway tunnel section is provided, by carrying out match in the data input sectional model that will gather, the error between calculated value and the actual measurement data is very little, can be applied in the real work fully.And simple to operate, easy to use, saved the field process time greatly, improved work efficiency.

The present invention realizes that the technical scheme of above-mentioned purpose is: a kind of measurement of subway tunnel section and computing method may further comprise the steps:

1) calculate the tunnel line centre coordinate, setting-out is in the tunnel;

2) settle the non-prism total powerstation on the tunnel center line;

3), calculate the elevation of sight of total powerstation, input non-prism total powerstation with the known point backsight and measure the discrepancy in elevation;

4) gather the section circle and go up the observation station coordinate, deposit it in total powerstation;

5) the non-prism total powerstation is gathered the section circle once more and is gone up observation station coordinate and storage along transverse axis Rotate 180 degree;

6) carry out the sectional model match according to the data of gathering;

7) calculate institute's match round center of circle and radius;

8) according to the center of circle and needed elevation of radius calculation and chord length.

Preferably, the sectional model of described step 6) is:

，i＝1，2，3，......，n (1)

With formula (1) linearization,, all regard it as variable during differential because each amount all is uncertain amount:

Then have:

$\frac{(y_i-y_0)\·V_{y_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}+\frac{(z_i-z_0)\·V_{z_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\frac{(y_i-y_0)\·{\mathrm{\δy}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}$

$-\frac{(z_i-z_0)\&CenterDot;{\mathrm{\&delta;z}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\mathrm{\&delta;r}+\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">r</figure-callout>}}_0=0---\left(3\right)$

Order:

$\frac{(y_i-y_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=a_i,$ $\frac{(z_i-z_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=b_i,$ $\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">r</figure-callout>}}_0=W_i$

Then have:

$a_i{V}_{y_i}+b_i{V}_{z_i}-a_i\mathrm{\&delta;}{y}_0-b_i\mathrm{\&delta;}{z}_0-\mathrm{\&delta;r}+W_i=0,$ i＝1，2，3，......，n (4)

δ y wherein ₀, δ z ₀Be the correction of central coordinate of circle unknown number,

Be that circle is gone up observation station coordinate correction number;

To justify and go up in the observation station coordinate substitution formula (4), obtain:

AV+BX+W＝0 (5)

Wherein, A is that the round observation station coordinate correction of going up is counted the factor arrays matrix, and B is central coordinate of circle and radius correction matrix, and X represents the unknown number matrix, and V is that circle is gone up observation station coordinate correction matrix number;

In the formula: $A=\left(\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\\ .& .\\ .& .\\ .& .\\ a_n& b_n\end{array}\right),$ $B=\left(\begin{array}{ccc}-a_1& -b_1& -1\\ -a_2& -b_2& -1\\ .& .& .\\ .& .& .\\ .& .& .\\ -a_n& -b_n& -1\end{array}\right),$ W＝W _i， $V=\left(\begin{array}{c}{V}_{y_1}\\ {\mathrm{<figure-callout\; id="1"\; label="V\; z"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">V</figure-callout>}}_{z_{}}\\ .\\ .\\ .\\ V_{y_n}\\ V_{z_n}\end{array}\right),$ $X=\left(\begin{array}{c}\mathrm{\&delta;y}\\ \mathrm{\&delta;z}\\ \mathrm{\&delta;z}\end{array}\right)$

At V ^TDraw under the PV=min condition: V=P ^-1A ^TK, B ^TK=0, wherein K is a correlate, in the substitution formula (5), obtains:

B is central coordinate of circle and radius correction matrix, and P is a weight matrix, considers it is equal observation, and I is a unit matrix.

$\left(\begin{array}{cc}N& \mathrm{<figure-callout\; id="0"\; label="B\; B\; T"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">B</figure-callout>}& \\ B^T{}^{}& 0\end{array}\right)\&CenterDot;\left(\begin{array}{c}K\\ X\end{array}\right)+\left(\begin{array}{c}\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">W</figure-callout>}\\ 0\end{array}\right)=0---\left(6\right)$

Wherein: P=I, N=AP ^-1A ^T

B is central coordinate of circle and radius correction matrix, and P is a weight matrix, and I is a unit matrix;

Order: $\left(\begin{array}{cc}{Q}_{11}& Q_{12}\\ Q_{21}& Q_{22}\end{array}\right)={\left(\begin{array}{cc}N& B\\ B^T& 0\end{array}\right)}^{-1}=\left(\begin{array}{cc}{N}^{-1}-R& N^{-1}B{M}^{-1}\\ M^{-1}{B}^T{N}^{-1}& -M^{-1}\end{array}\right)$

In the formula: M=B ^TN ^-1B, R=N ^-1BM ^-1B ^TN ^-1

Then: $\left(\begin{array}{c}K\\ X\end{array}\right)=\left(\begin{array}{cc}{Q}_{11}& Q_{12}\\ Q_{21}& Q_{22}\end{array}\right)\&CenterDot;\left(\begin{array}{c}\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">W</figure-callout>}\\ 0\end{array}\right),$ That is: K=-Q ₁₁W, X=-Q ₂₁W (7)

The present invention makes it compared with prior art owing to adopted above technical scheme, has the following advantages and good effect:

The data reliability that the inventive method records is very high, and the error between the actual measurement data is very little, can be applied in the real work fully.And simple to operate, easy to use, saved the field process time greatly, improved work efficiency.

The present invention is not only applicable to the acceptance survey of subway tunnel, is applicable to other similar Tunnel Engineering (as vcehicular tunnel holing-through survey, down-hole mining tunnel measurement etc.) yet, and can be widely used in large tunnel construction enterprises, tunnel excavation job design unit etc.

Description of drawings

Fig. 1 is the coordinate system sketch of subway tunnel section of the present invention.

Embodiment

In the section survey in tunnel, because section is one circle in theory, but because the error of practice of construction, section can not be the circle of a standard and approximate circle just.Approach actual circle in order to seek a standard round, set up coordinate system as shown in Figure 1 for convenience of explanation.

Present embodiment mainly adopts the non-prism total powerstation to carry out tunnel cross-section measurement.As requested, the tunnel is at the every 10m of straight-line segment, and the every 5m of segment of curve should survey and establish a transversal section, and the position of tunnel cross section point should be the gauge reference mark.According to standard, the mileage permissible error of measuring section point should be at ± 50mm, and section survey precision permissible error is ± 10mm that the elevation permissible error is ± 10mm.

The operation steps of present embodiment is as follows:

1) calculate the tunnel line centre coordinate, setting-out is in the tunnel;

Promptly, calculate the coordinate of route mid point (every 10m or 5m), go out centerline according to reference mark (plane and the elevation) setting-out that provides then, measure the elevation of institute's setting-out centerline by the fourth-order leveling requirement according to the circuit drawing that provides.

2) settle the non-prism total powerstation on the tunnel center line;

Promptly adopt the non-prism total powerstation (Topcon GTS 6002, ± 2 " ± 2mm+2ppm) be placed in the centerline of institute's setting-out, with the known point backsight and measure the discrepancy in elevation, calculate the elevation of sight of non-prism total powerstation.

3) elevation input non-prism total powerstation;

4) rotate the non-prism total powerstation and (can precompute the anglec of rotation) to vertical plane, observation station coordinate and non-prism deposit total powerstation on the some circles of random acquisition;

5) the non-prism total powerstation is gathered circle once more and is gone up observation station coordinate and storage along transverse axis Rotate 180 degree;

As shown in Figure 1, generally on circumference, gather the 10-15 point.No. 1 point adopts elder generation that total powerstation is transferred to plumbness and measures oblique distance again, can calculate three-dimensional coordinate.In order to guarantee the fitting precision of circle, on the circumference about the indivedual points in below as total powerstation can replace with reflector plate because of can't find range the time apart from too short non-prism.

6) carry out the sectional model match according to the data of gathering;

7) calculate institute's match round center of circle and radius;

8) according to the center of circle and needed elevation of radius calculation and chord length.

As shown in Figure 1, can be according to 1 and 6 center approximate coordinates (y that determine circle ₀, z ₀) and radius r ₀, determining step 6) sectional model be:

，i＝1，2，3......，n (1)

With formula (1) linearization,, all regard it as variable during differential because each amount of formula (1) all is uncertain amount:

Then have:

$\frac{(y_i-y_0)\&CenterDot;V_{y_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}+\frac{(z_i-z_0)\&CenterDot;V_{z_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\frac{(y_i-y_0)\&CenterDot;{\mathrm{\&delta;y}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}---\left(3\right)$

$-\frac{(z_i-z_0)\&CenterDot;{\mathrm{\&delta;z}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\mathrm{\&delta;r}+\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">r</figure-callout>}}_0=0$

Order:

$\frac{(y_i-y_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=a_i,$ $\frac{(z_i-z_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=b_i,$ $\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">r</figure-callout>}}_0=W_i$

Then have:

$a_i{V}_{y_i}+b_i{V}_{z_i}-a_i\mathrm{\&delta;}{y}_0-b_i\mathrm{\&delta;}{z}_0-\mathrm{\&delta;r}+W_i=0,$ i＝1，2，3，......，n (4)

δ y wherein ₀, δ z ₀Be the correction of central coordinate of circle unknown number,

Be that circle is gone up observation station coordinate correction number;

To justify and go up in the observation station coordinate substitution formula (4), obtain:

AV+BX+W＝0 (5)

Wherein, A is that the round observation station coordinate correction of going up is counted the factor arrays matrix, and B is central coordinate of circle and radius correction matrix, and X represents the unknown number matrix, and V is that circle is gone up observation station coordinate correction matrix number;

In the formula: $A=\left(\begin{array}{cc}{a}_1& b_1\\ a_2& {\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">b</figure-callout>}}_2\\ .& .\\ .& .\\ .& .\\ a_n& b_n\end{array}\right),$ $B=\left(\begin{array}{ccc}-a_1& -b_1& -1\\ -a_2& -b_2& -1\\ .& .& .\\ .& .& .\\ .& .& .\\ -a_n& -b_n& -1\end{array}\right),$ W＝W _i， $V=\left(\begin{array}{c}{V}_{y_1}\\ {\mathrm{<figure-callout\; id="1"\; label="V\; z"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">V</figure-callout>}}_{z_{}}\\ .\\ .\\ .\\ V_{y_n}\\ V_{z_n}\end{array}\right),$ $X=\left(\begin{array}{c}\mathrm{\&delta;y}\\ \mathrm{\&delta;z}\\ \mathrm{\&delta;z}\end{array}\right)$

At V ^TDraw under the PV=min condition: V=P ^-1A ^TK, B ^TK=0, wherein K is a correlate, in the substitution formula (5), obtains:

$\left(\begin{array}{cc}N& \mathrm{<figure-callout\; id="0"\; label="B\; B\; T"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">B</figure-callout>}& \\ B^T{}^{}& 0\end{array}\right)\&CenterDot;\left(\begin{array}{c}K\\ X\end{array}\right)+\left(\begin{array}{c}\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">W</figure-callout>}\\ 0\end{array}\right)=0---\left(6\right)$

Wherein: P=I, N=AP ^-1A ^T

B is central coordinate of circle and radius correction matrix, and P is a weight matrix, considers it is equal observation, and I is a unit matrix;

Order: $\left(\begin{array}{cc}{Q}_{11}& Q_{12}\\ Q_{21}& Q_{22}\end{array}\right)={\left(\begin{array}{cc}N& B\\ B^T& 0\end{array}\right)}^{-1}=\left(\begin{array}{cc}{N}^{-1}-R& N^{-1}B{M}^{-1}\\ M^{-1}{B}^T{N}^{-1}& -M^{-1}\end{array}\right)$

In the formula: M=B ^TN ^-1B, R=N ^-1BM ^-1B ^TN ^-1

Then: $\left(\begin{array}{c}K\\ X\end{array}\right)=\left(\begin{array}{cc}{Q}_{11}& Q_{12}\\ Q_{21}& Q_{22}\end{array}\right)\&CenterDot;\left(\begin{array}{c}\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="A2008102006060011H1.png"\; state="\{\{state\}\}">W</figure-callout>}\\ 0\end{array}\right),$ That is: K=-Q ₁₁W, X=-Q ₂₁W (7)

Observation station measurement of coordinates data are as follows on the circle of present embodiment section random acquisition:

Table 1 subway profile data meter

Round approximate center coordinate and radius (29406.7695 ,-0.7125,2.75) can be calculated by above-mentioned mathematical model coding, correlate can be calculated earlier by least square method (formula 6,7):

K＝(14.4?6.19?-17.2?-15.0?-14.35?-10.2?13.4?13.4) ^T，

If repeatedly observe one or more unknown quantitys with different accuracy, in order to ask the reliable value of fixed each unknown quantity, each observed quantity must add correction, and the summation of the flexible strategy that square multiply by observed reading that makes its each correction is for minimum.Therefore claim least square method.So-called " power " is exactly to represent a kind of trade-off value of the relative degree of reliability of observed result quality.

And the probability value that can calculate the correction of unknown number and approximate coordinates, radius is

δy＝4.9mm，δz＝-14.3mm，δr＝19.5mm。

The equation of a circle that utilization calculates

The height above rail surface-2.573 of the actual measurement elevation-3.466 of centre bottom and design can calculate the chord length of 3.67 meters elevations and 4.26 meters elevation places on height above rail surface, the rail level.Concrete computational data and comparative observation data see the following form:

Table 2 subway circular cross section elevation and transfer are measured contrast table

Be noted that above enumerate only for specific embodiments of the invention, obviously the invention is not restricted to above embodiment, many similar variations are arranged thereupon.If those skilled in the art all should belong to protection scope of the present invention from all distortion that content disclosed by the invention directly derives or associates.

Claims (2)

1. the measurement of a subway tunnel section and computing method is characterized in that may further comprise the steps:

1) calculate the tunnel line centre coordinate, setting-out is in the tunnel;

2) settle the non-prism total powerstation on the tunnel center line;

3), calculate the elevation of sight of total powerstation, input non-prism total powerstation with the known point backsight and measure the discrepancy in elevation;

4) gather the section circle and go up the observation station coordinate, deposit it in total powerstation;

5) the non-prism total powerstation is gathered the section circle once more and is gone up observation station coordinate and storage along transverse axis Rotate 180 degree;

6) carry out the sectional model match according to the data of gathering;

7) calculate institute's match round center of circle and radius;

8) according to the center of circle and needed elevation of radius calculation and chord length.

2. the measurement of subway tunnel section as claimed in claim 1 and computing method, it is characterized in that: the sectional model of described step 6) is:

i＝1，2，3......，n (1)

With formula (1) linearization,, all regard it as variable during differential because each amount all is uncertain amount:

Then have:

$\frac{(y_i-y_0)\&CenterDot;V_{y_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}+\frac{(z_i-z_0)\&CenterDot;V_{z_i}}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\frac{(y_i-y_0)\&CenterDot;{\mathrm{\&delta;y}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}$

$-\frac{(z_i-z_0)\&CenterDot;{\mathrm{\&delta;z}}_0}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}-\mathrm{\&delta;r}+\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-r_0=0---\left(3\right)$

Order:

$\frac{(y_i-y_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=a_i,$ $\frac{(z_i-z_0)}{\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}}=b_i,$ $\sqrt{{(y_i-y_0)}^2+{(z_i-z_0)}^2}-r_0=W_i$

Then have:

$a_i{V}_{y_i}+b_i{V}_{z_i}-a_i\mathrm{\&delta;}{y}_0-b_i\mathrm{\&delta;}{z}_0-\mathrm{\&delta;r}+W_i=0,$ i＝1，2，3，......，n (4)

δ y wherein ₀, δ z ₀Be the correction of central coordinate of circle unknown number,

Be that circle is gone up observation station coordinate correction number;

To justify and go up in the observation station coordinate substitution formula (4), obtain:

AV+BX+W＝0 (5)

Wherein, A is that the round observation station coordinate correction of going up is counted the factor arrays matrix, and B is central coordinate of circle and radius correction matrix, and X represents the unknown number matrix, and V is that circle is gone up observation station coordinate correction matrix number;

In the formula:

W=W _i,

At V ^TDraw under the PV=min condition: V=p ^-1A ^TK, B ^TK=0, wherein K is a correlate, in the substitution formula (5), obtains:

$\left(\begin{array}{cc}N& B\\ B^T& 0\end{array}\right)\&CenterDot;\left(\begin{array}{c}K\\ X\end{array}\right)+\left(\begin{array}{c}W\\ 0\end{array}\right)=0---\left(6\right)$

Wherein: P=I, N=AP ^-1A ^T

B is central coordinate of circle and radius correction matrix, and P is a weight matrix, and I is a unit matrix;

Order: $\left(\begin{array}{cc}{Q}_{11}& Q_{12}\\ Q_{21}& Q_{22}\end{array}\right)={\left(\begin{array}{cc}N& B\\ B^T& 0\end{array}\right)}^{-1}=\left(\begin{array}{cc}{N}^{-1}-R& N^{-1}{\mathrm{BM}}^{-1}\\ M^{-1}{B}^T{N}^{-1}& -M^{-1}\end{array}\right)$

In the formula: M=B ^TN ^-1B, R=N ^-1BM ^-1B ^TN ^-1

Then: That is: K=-Q ₁₁W, X=-Q ₂₁W.(7)

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