CN102155230A - Tunnel curve segment lofting method based on circle coordinates - Google Patents
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Abstract
The invention discloses a tunnel curve segment lofting method based on circle coordinates, which is characterized in that the method comprises the following steps of: step 1. preparation step: determining the positions of an original point of a measuring-coordinate system and a circle center O (a, b) of a tunnel curve segment, and establishing the measuring-coordinate system, namely, an XOY coordinate system; step 2: lofting step: obtaining coordinates (x, y) of a measuring point at a cross section, calculating the value of (x-a)2+(y-b)2-r2, namely, a calculated value, wherein r represents the radius of the tunnel curve segment; moving the position of the measuring point according to the size and the plus-minus of the calculated value, updating the coordinates (x, y) of the measuring point till determining points of intersections of the cross section with an axis, an inner arc and an outer arc, thus finishing the lofting of the cross section; step 3. in the tunneling process of the tunnel curve segment, repeating the step 2, and finishing the lofting of the whole tunnel curve segment. The tunnel curve segment lofting method based on the circle coordinates has less calculated amount, is easy to implement and has high lofting precision.
Description
Technical field
The invention belongs to the underground engineering construction field, relate to a kind of tunnel curved section setting out method based on circle coordinates.
Background technology
In engineering construction, tunnel curved section setting-out is the emphasis difficult point of surveying work, also is the important step that influences the tunnel holing through precision, guarantees workmanship.Tunnel curve setting-out is basic identical with the content of curve setting-out outside the venue, except obvious characteristic points such as the point of curve that will measure curve, Qu Zhongdian, point of tangent, also to establish the auxiliary magnet on the circular curve in (2m, 3m or any rice) survey at a certain distance on the curve, again these auxiliary magnets are connected with smooth curve, like this could the shape of curve and position exactly setting-out on the spot.Compare ground surface curve engineering, the tunnel curve is positioned at underground, and setting-out elements such as the curve center of circle and corner have only numerical value, so the setting-out difficulty of tunnel curve is bigger, it is higher to require.
Traditional curved section setting-out mainly contains the method for deflection angle and the method for tangent offsets etc., because these method amounts of calculation are big, shortcomings such as the setting-out step is many, and because of method difference that the surveyor grasped, often there be the setting out method difference of same tunnel curved section because of using, cause outer arc side wall faulting of slab ends in the tunnel curved section, cause poor (the wheel hub line of side wall when territory is meant tunnel piercing of curve territory shaping, when using the boring of jumbo and air drill, drill bit is all aimed at this line, the hole that gets out will be on a face, side wall just can be very straight like this, vault also can be very smooth, perimeter line when in fact being exactly highway tunnel construction), the setting-out precision is low, shortcomings such as piercing error is big have had a strong impact on the set of tunneling construction quality.
Summary of the invention
Technical problem to be solved by this invention is to propose a kind of tunnel curved section setting out method based on circle coordinates, should be little, easy to implement based on the tunnel curved section setting out method amount of calculation of circle coordinates, and setting-out precision height.
Technical solution of the present invention is as follows:
A kind of tunnel curved section setting out method based on circle coordinates comprises the steps:
Step 1: preparation process: determine that (setting up measurement coordinate system is the XOY coordinate system for a, position b) for the center of circle O of measurement coordinate system initial point and tunnel curved section;
Step 2: setting-out step: (x y), calculates (x-a) coordinate of acquisition section part measuring point
2+ (y-b)
2-r
2Value be calculated value, wherein r is the radius of tunnel curved section; According to the size and the positive and negative mobile point position of this calculated value, and (x y), up to this section of determining the tunnel curved section and the intersection point of axis, inner arc and outer arc, finishes the setting-out of a section to upgrade the measuring point coordinate;
(x0 y0) satisfies: (x0-a) intersection point of this section and axis
2+ (y0-b)
2-r
2=0;
(x1 y1) satisfies: (x1-a) intersection point of this section and inner arc
2+ (y1-b)
2-(r-d/2)
2=0, wherein d is the section span;
(x2 y2) satisfies: (x2-a) intersection point of this section and outer arc
2+ (y2-b)
2-(r+d/2)
2=0, wherein d is the section span;
Step 3: in the tunneling process of tunnel curved section, repeating step 2 is finished the setting-out of whole tunnel curved section;
In the described step 1, the known coordinate point in the tunnel sets up total powerstation, requires total powerstation can observe the section of tunnel curved section, places prism at the measuring point place of described section, is recorded the coordinate of measuring point by total powerstation and prism; Tunnel direction of advance with the section start of tunnel curved section is the direction of a coordinate axes of measurement coordinate system.
The origin of coordinates is chosen on the starting point of the center of circle or tunnel curved section, when the origin of coordinates is chosen on the center of circle, a=0, b=0 is arranged then; Be chosen in when the origin of coordinates on the starting point of tunnel curved section, a=-50 then arranged, b=0.
In fact, can also select other points, just adopt aforesaid two positions to set up coordinate system and calculate more easy as the coordinate center.
Technical conceive:
Circle coordinates method operating principle
The operating principle of circle coordinates method is: the tunnel curve also is the part of circular curve, and the more any coordinate on its curve all should be followed round normal equation: (x-a)
2+ (y-b)
2=r
2, wherein x, y are the coordinate of the point on the curve, a, b are that central coordinate of circle, r are radius.When we are assumed to be the measurement origin of coordinates with the curve center of circle, tunnel, the normal equation (x-a) of circle
2+ (y-b)
2=r
2Middle a, b=0 can be deformed into x
2+ y
2=r
2We utilize the cosine law of right-angled triangle: a again
2+ b
2=c
2(a, b, c are respectively two right-angle sides and hypotenuse length of side value).
After dexterously the relative position in the coordinate of measuring point and the center of circle, tunnel being switched, by these two formula, the coordinate Calculation of arbitrfary point on inside and outside arc in tunnel and the axis can be come out again, and accurately setting-out goes out the inside and outside arc and the axis of tunnel curve.(measurement coordinate system that will note and mathematics coordinate system are inequality, x, and y is inverted.)
Beneficial effect:
Tunnel curved section setting out method based on circle coordinates of the present invention is original a kind of method in the constructing tunnel field, and engineering practice shows that it is little that this method has amount of calculation, and step is simple and easy, and is easy to implement, outstanding features such as precision height, and concrete mark is as follows:
(1) survey section in this way, instrument can not be erected at the point of contact, also can be not on circular curve, can on known coordinate point arbitrarily, utilize the relativeness of measuring point and circular curve, and mobile again measuring point is finally determined the accurate position of outer arc and center line in the section;
(2) used formula is very simple, easy, and amount of calculation is less simultaneously, is not easy to make mistakes;
(3) adopt the inventive method, the setting-out precision is the highest, and the more preceding several method of the precision of setting-out is all accurate in this way, and in the practical application, the axis piercing error is less than 5mm.
The curved section setting out method comparative analysis of several tunnels
According to constructing tunnel experience for many years, several tunnels curved section setting out method commonly used is compared, as following table:
When carrying out tunnel curved section measurement, except need are taken all factors into consideration by the factors such as restriction of working space to sweep, curve arc long, hair hole span and chassis drill boom length and drill boom thereof, also to guarantee that tunnel curved section axis is constant, outer arc side wall out break in controlling well simultaneously.Therefore determine that every big gun drilling depth, boring direction, drilling depth dead line etc. all become accurately, the key factor of quick setting-out tunnel curved section.
Because the method for tunnel curved section setting-out is more, when used setting out method is inconsistent, can cause the cross section place of institute's setting-out that certain difference is arranged simultaneously, influence the section territory and be shaped.In tunnel curved section setting-out process in the past, once inconsistent because of the employed setting out method of surveyor, and cause two big gun setting-outs up and down that the faulting of slab ends of 5～10cm is arranged, add the chassis bore angle to be difficult to hold, and cause entire curve section shaping irregularity.
Thereby, can accurately determine each section of tunnel curved section, be to guarantee that axis is accurate, the territory regular key factor that is shaped.In the construction of tunnel curved section, unified employing this circle coordinates method simple, understandable, that precision is high is carried out setting-out, efficiently solve difficult problems such as arc setting-out difficulty is big, out break control is difficult, design formulas is numerous and diverse, the setting-out time shortened to 1 hour by original 2,3 hours simultaneously, had improved effect greatly.
Description of drawings
Fig. 1 is pairing each point coordinates of drawing coordinate system and position view;
Fig. 2 is based on pairing each point coordinates of the measurement coordinate system of center of circle circle coordinates and position view;
Fig. 3 is the schematic diagram of the calculated examples correspondence among the embodiment 1;
Fig. 4 is the measurement coordinate system sketch based on the point of contact coordinate method;
Fig. 5 is based on pairing each point coordinates of the measurement coordinate system of point of contact circle coordinates and position view;
Fig. 6 is the schematic diagram of the calculated examples correspondence among the embodiment 2.
Among Fig. 1, Fig. 2 and Fig. 5, the A point is the stake point, and B is the origin of curve, and among Fig. 3 and Fig. 6, C is a measuring point, and E is the point of contact.
The specific embodiment
Below with reference to the drawings and specific embodiments the present invention is described in further details:
According to the initial point difference of assumed coordinate system, the circle coordinates method can be divided into two kinds of point of contact circle coordinates method, center of circle circle coordinates methods again, and its difference is that the origin of coordinates that the point of contact coordinate method is supposed is the curve point of contact, and the origin of coordinates that the central coordinate of circle method is supposed is the curve center of circle.
Embodiment 1:
Center of circle circle coordinates method is called for short the central coordinate of circle method.
The basic step of its setting-out is:
The first step: set up total powerstation on the stake point of known coordinate in the tunnel, require total powerstation energy observation curve section section, total powerstation is the instrument that is used to put the territory line, and model has a lot, adopts Switzerland's come card total powerstation in the present embodiment.So-called total powerstation is to put primary line need not move instrument, and a station just can be finished, and will repeatedly adjust, set up prism at measuring point unlike transit; Prism is the auxiliary equipment of total powerstation, and it comes down to a reflecting optics, during measurement it is installed on the prism bar, be placed on the some position that needs to measure, total powerstation is aimed at it and is penetrated beam of laser, and this Shu Jiguang returns by prismatic reflection, and total powerstation just can draw the coordinate of that some position; According to the data that drawing or control survey provide, to change according to the relativeness in the stake point and the center of circle again, the coordinate transform example is as follows.
The mileage of stake point A is that (its expression is 2100 meters from starting point to this position to K2+100m, K is first letter of Kilometer, writing like this is a kind of way of specialty regulation), curved section starting point mileage is K2+160m, the curved section radius is R=50m, curve center of circle O point is for measuring the origin of coordinates, as shown in Figure 1
The coordinate of supposing the road starting point is (0,0), and according to the mileage K2+100 of stake point A, then can change the drawing coordinate into is (2100,0), in like manner, the coordinate of curved section starting point B can change (2160 into, 0), the coordinate of curved section centre point O is (2160 ,-50) [central coordinate of circle is a known quantity].
According to the relation of known conditions and last figure each point, then can carry out the conversion (coordinate system conversion is not a necessary step, can adopt measurement coordinate system at the very start yet, so just needn't coordinate transform) of drawing coordinate system and measurement coordinate system:
In the drawing coordinate, the direction of advance of road is the positive direction of coordinate X-axis, and in measurement coordinate system, still the direction of advance with road is the positive direction of X-axis, known again curve center of circle O point is the measurement coordinate system initial point, only needs that then the drawing coordinate origin is moved to the measurement coordinate system initial point and gets final product.Its corresponding relation can be converted into: the coordinate of curved section centre point O is (0,0), and the coordinate of curved section starting point B is (0,50), and then the drawing coordinate of stake point A is (60,50), sees Fig. 2.
Several points to note:
(1) kilometer stone of road in the drawing coordinate, the direction of advance of road is the positive direction of coordinate X-axis, from the off, on its road axes more arbitrarily, no matter whether road turns round, the coordinate of this point can with (X, 0) expression.
(2) in measurement coordinate system, the origin of coordinates is in the curve center of circle, then the coordinate of the origin of curve be (0, ± R), R is the turning radius of curve, and curved section is with the difference of center line of road yawing moment, and R has positive and negative branch, and curve is turned left, R be on the occasion of, curve is turned right, R is a negative value.
(3) institute's survey prism point no matter in any position all can, these two kinds of coordinate systems can both be changed, can calculate this coordinate with respect to the curved section center of circle (initial point) of hypothesis.
Second step: can set up total powerstation on the point of observation curve section section what previous step was surveyed earlier, import the relative coordinate that this puts the corresponding curve center of circle (initial point) again, with the road curve tangential direction is the positive direction of coordinate system, measure the various parameters of curved section section, according to the circle coordinates ratio juris, the point coordinates that makes it to be surveyed on the axis satisfies round reduced equation: x
2+ y
2=r
2In like manner, according to section span (d), then inside and outside arc institute respective radius is r-d/2, r+d/2.Same available formula x
2+ y
2=r
2Obtain on the inside and outside arc the accurate position of any arbitrarily.X, y are by being surveyed x, y value in the corresponding measurement coordinate system in the formula, and r can distinguish the inside and outside arc of corresponding curve or the radius of axis.
Calculated examples: circular curve radius R=50m, span is 4.6m, sets up instrument, imports the relative coordinate that this puts the corresponding center of circle, the coordinate of measuring point C be (9.346,51.459), as shown in Figure 3,
Will be at the coordinate of measuring point C, the design formulas of its central coordinate of circle method of substitution: x
2+ y
2=r
2, can get (9.346
2+ (51.459)
2)-(50+2.3)
2=0, this explanation institute measuring point is just on the outer arc of curved section.
Therefore, can pass through formula x
2+ y
2-r
2Whether equal zero and judge that institute's measuring point is whether on the inside and outside arc and axis of curved section.Sign according to amount of movement is judged the direction that measuring point moves, and its determination methods is:
(1) x
2+ y
2-r
2=0, illustrate that then institute's measuring point is on the inside and outside arc or axis of curved section;
(2) x
2+ y
2-r
2＞0, institute's measuring point then is described not on the inside and outside arc or axis of curved section, institute's measuring point needs to move toward curve center of circle direction, and movement value (is x for the value of calculating gained
2+ y
2-r
2Value, down with) the extraction of square root value;
(3) x
2+ y
2-r
2＜0, institute's measuring point then is described not on the inside and outside arc or axis of curved section, institute's measuring point needs to move toward the direction away from the curve center of circle, and movement value is the extraction of square root value of the value of calculating gained;
Through repeatedly observing the position of measuring point, and by formula x
2+ y
2=r
2Calculate, finally determine to satisfy the axis of curve, the position of interior outer arc.By practice, general only the need moved 2～3 times, can measure and satisfy in the inside and outside arc of curved section or the exact position on the axis.
Embodiment 2:
Point of contact circle coordinates method is called for short the point of contact coordinate method.
Point of contact coordinate method setting out method and step concentric coordinate method are basic identical, unique different a bit, be exactly its origin of coordinates be the point of contact, circle coordinates method formula x
2+ y
2=r
2Then can develop into the design formulas r of point of contact coordinate method
2=x
2+ (r-|y|)
2(measurement coordinate system sketch such as Fig. 4 of point of contact coordinate method) or employing formula (x-a)
2+ (y-b)
2=r
2, wherein (a b) is central coordinate of circle.
The point of contact coordinate method is after drawing coordinate system and measurement coordinate system conversion, and its coordinate of surveying is the coordinate at relative point of contact, calculates the position in the relative center of circle of being surveyed of point and will pass through r
2=x
2+ (r-|y|)
2Calculate, its survey station method, calculation procedure are basic identical with relevant determination methods concentric coordinate method, comparative examples 1, and those of ordinary skill in the art knows how to implement, do not describe in detail at this fully.
Calculated examples: can observation curve the section section set up total powerstation more arbitrarily, the coordinate of the measuring point C of institute is (44.680 ,-13.799), circular curve radius R=70m is as Fig. 6.
According to formula: r
2=x
2+ (r-|y|)
2Can get
(44.682
2+ (70-13.799)
2)-70
2=1.797m
2, institute's measuring point moves sqrt (1.797) m toward center of circle direction and is the curve center line.
Other application of the inventive method:
The circle coordinates method is except that the utilization of straight circular arch tunnel, tunnel curved section, can also be used to elliptic arch, the inverted arch of setting-out tunnel curved section, its method is: whole section is divided into n height by perimeter hole spacing or every 0.5m (1m), calculate the radius (outer arc in dividing) of each point then respectively, according to the radius calculation institute measuring point of each height, carry out setting-out again.During setting-out, the departing from constant and will calculate (the pairing radius of each point is inconsistent) separately of the chassis of each point boring.But the direction value of the axial symmetry point up and down of section is got same value.When radius is very big, and the variation of each point radius is neither be very big the time, also desirable same value.All will change with the variation of height when general, the chassis drilling accuracy just can be high like this.
In addition, the method equally also can directly be used for the arbitrfary point of the known curve in setting-out ground.
Claims (2)
1. the tunnel curved section setting out method based on circle coordinates is characterized in that, comprises the steps:
Step 1: preparation process: determine that (setting up measurement coordinate system is the XOY coordinate system for a, position b) for the center of circle O of measurement coordinate system initial point and tunnel curved section;
Step 2: setting-out step: (x y), calculates (x-a) coordinate of acquisition section part measuring point
2+ (y-b)
2-r
2Value be calculated value, wherein r is the radius of tunnel curved section; According to the size and the positive and negative mobile point position of this calculated value, and (x y), up to this section of determining the tunnel curved section and the intersection point of axis, inner arc and outer arc, finishes the setting-out of a section to upgrade the measuring point coordinate;
(x0 y0) satisfies: (x0-a) intersection point of this section and axis
2+ (y0-b)
2-r
2=0;
(x1 y1) satisfies: (x1-a) intersection point of this section and inner arc
2+ (y1-b)
2-(r-d/2)
2=0, wherein d is the section span;
(x2 y2) satisfies: (x2-a) intersection point of this section and outer arc
2+ (y2-b)
2-(r+d/2)
2=0, wherein d is the section span;
Step 3: in the tunneling process of tunnel curved section, repeating step 2 is finished the setting-out of whole tunnel curved section;
In the described step 1, the known coordinate point in the tunnel sets up total powerstation, requires total powerstation can observe the section of tunnel curved section, places prism at the measuring point place of described section, is recorded the coordinate of measuring point by total powerstation and prism; Tunnel direction of advance with the section start of tunnel curved section is the direction of a coordinate axes of measurement coordinate system.
2. the tunnel curved section setting out method based on circle coordinates according to claim 1 is characterized in that the origin of coordinates is chosen on the starting point of the center of circle or tunnel curved section, when the origin of coordinates is chosen on the center of circle, a=0, b=0 is arranged then; Be chosen in when the origin of coordinates on the starting point of tunnel curved section, a=-50 then arranged, b=0.
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| CN109211167B (en) * | 2018-09-03 | 2021-06-01 | 山东大学 | Tunnel secondary lining thickness accurate detection method based on function curve fitting |
| CN109184702A (en) * | 2018-09-21 | 2019-01-11 | 中国建筑第八工程局有限公司 | The measurement method of out break is controlled under the conditions of the more curves of Tunnel Engineering, minor radius |
| CN112528217A (en) * | 2020-12-22 | 2021-03-19 | 中电建十一局工程有限公司 | Parabolic same-layer equal-thickness arch dam measurement lofting calculation method |
| CN112528217B (en) * | 2020-12-22 | 2024-08-27 | 中电建十一局工程有限公司 | Parabolic same-layer equal-thickness arch dam measurement lofting calculation method |
| CN113137952A (en) * | 2021-04-23 | 2021-07-20 | 交通运输部公路科学研究所 | Positioning method for tunnel section measuring point |
| CN113137952B (en) * | 2021-04-23 | 2021-11-12 | 交通运输部公路科学研究所 | Positioning method for tunnel section measuring point |
| CN114863385A (en) * | 2022-03-23 | 2022-08-05 | 禾多科技（北京）有限公司 | Road curved surface information generation method, device, equipment and computer readable medium |
| CN114863385B (en) * | 2022-03-23 | 2023-04-07 | 禾多科技（北京）有限公司 | Road curved surface information generation method, device, equipment and computer readable medium |
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