CN108896015B - Double-laser collimation measuring method for tunnel structural surface attitude - Google Patents
Double-laser collimation measuring method for tunnel structural surface attitude Download PDFInfo
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- CN108896015B CN108896015B CN201810549425.6A CN201810549425A CN108896015B CN 108896015 B CN108896015 B CN 108896015B CN 201810549425 A CN201810549425 A CN 201810549425A CN 108896015 B CN108896015 B CN 108896015B
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- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C7/00—Tracing profiles
- G01C7/06—Tracing profiles of cavities, e.g. tunnels
Abstract
Discloses a double-laser collimation measuring method for tunnel structural plane attitude, belonging to the technical field of geotechnical mechanical testing. The measuring method comprises the following steps: establishing a measuring coordinate system taking the axis direction of the tunnel as a Y axis and the zenith direction as a Z axis; determining the position of the origin of the measurement coordinate system at the cross section of the tunnel according to the parallel distance between the total station and the wall surface of the tunnel and the diameter of the tunnel when the horizontal azimuth angles are 0 ' and 180 ' 0 '; acquiring local coordinates of characteristic points of a track line of a tunnel structural surface; connecting the characteristic points until the number of the characteristic points reaches 3 or more, and obtaining exposed traces of the same structural surface of the tunnel; repeating the steps to obtain exposed traces of all structural surfaces within the effective measuring distance of the measuring station; and carrying out post-processing on exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces. The method can provide necessary basic information for searching key blocks of the surrounding rock of the tunnel and analyzing the stability of the surrounding rock.
Description
Technical Field
The invention relates to the technical field of geotechnical testing, in particular to a double-laser collimation measuring method for tunnel structural plane attitude.
Background
The deformation, strength and stability of the engineering rock mass are controlled by the rock mass structure; the occurrence of the structural plane is important basic information for describing the rock mass structure and is a basic basis for dividing different engineering geological units; meanwhile, the method is also an important geological parameter necessary for designing underground caverns, artificial slopes and dam foundations. Therefore, timely, accurate and systematic acquisition of the occurrence information of the structural plane has important guiding significance for investigation, design and construction of rock engineering.
The method is characterized in that a mechanical geological compass is adopted by a measurer to select a representative exposed part of a structural surface for measurement, reading and recording, and has the advantages of low measurement technology cost, simple tool and convenience in carrying.
The TBM (Tunnel Boring Machine) excavation belongs to non-blasting excavation, the damage and disturbance to rock mass are small, and the wall of a hole formed by excavation is smooth and flat; the structural surface generally presents a closed linear trace on the wall of the TBM hole; and because TBM hole diameter is great, the survey crew is difficult to direct contact exposed structural plane on the hole wall. Therefore, the traditional measuring method based on the geological compass is difficult to be applied to the TBM tunnel. For TBM tunnel sections without system support and lining design, the key block searching and analysis are carried out on the structural surface on the basis of system measurement, and the method has very important significance for guaranteeing the stability of surrounding rocks and the construction safety.
Disclosure of Invention
In view of the above, the invention provides a double-laser collimation measurement method for tunnel structural plane attitude, which can record the structural plane of a system for a tunnel formed by TBM excavation and acquire the structural plane attitude and trajectory network information, thereby providing necessary basic information for searching key blocks of surrounding rocks of the tunnel and analyzing the stability of the surrounding rocks, and being more practical.
In order to achieve the first object, the technical scheme of the double-laser collimation measuring method for the tunnel structural surface attitude provided by the invention is as follows:
the double-laser collimation measuring method for the tunnel structural surface attitude provided by the invention is realized under the condition of jointly applying a handheld laser device and a prism-free total station, and comprises the following steps:
leveling the total station and adjusting a telescope disposed on the total station such that a vertical angle reading of the telescope is horizontal 0 °;
adjusting the sight direction of the telescope, acquiring the position of the telescope with the minimum horizontal distance from the wall surface of the tunnel, defining the sight direction of the telescope as the direction vertical to the axis direction of the tunnel, and setting the horizontal azimuth angle of the sight direction of the telescope to be 0';
establishing a measuring coordinate system taking the axis direction of the tunnel as a Y axis and the zenith direction as a Z axis;
determining the position of the origin of the measurement coordinate system at the cross section of the tunnel according to the parallel distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 0 degrees 0 ', the parallel distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 180 degrees 0', and the diameter of the tunnel;
determining the position pile number of the total station through coordinate measurement of a control point, and simultaneously measuring the direction azimuth angle of the hole axis of the total station by using a geological compass to establish a survey station;
tracking the tunnel structure surface trace by using a handheld laser device and confirming the characteristic points of the tunnel structure surface trace;
rotating a lens of the total station, and locking the lens of the total station when a laser spot emitted by the total station is superposed with a laser spot emitted by the handheld laser device, so as to obtain local coordinates of characteristic points of the track of the tunnel structure surface;
repeating the step of obtaining the local coordinates of the feature points of the tunnel structural surface trace until the number of the feature points reaches 3 or more, and connecting the feature points to obtain an exposed trace of the same structural surface of the tunnel, wherein at least 3 feature points are non-collinear feature points in the exposed trace of the same structural surface of the tunnel;
repeating the steps to obtain exposed traces of all structural surfaces within the effective measuring distance of the measuring station;
and carrying out post-processing on the exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces.
The double-laser collimation measuring method for the tunnel structural surface attitude can be further realized by adopting the following technical measures.
Preferably, the method for adjusting the sight line direction of the telescope to obtain the azimuth with the minimum horizontal distance from the telescope to the wall surface of the tunnel comprises the following steps:
aiming the sight line direction of the telescope at the wall surface of the tunnel, so that the sight line of the telescope points to the axial direction perpendicular to the tunnel;
swinging the telescope left and right, recording the direction of the telescope, which is parallel to the wall surface of the tunnel, as a first direction, and recording the direction opposite to the first direction as a second direction;
the telescope is made to swing towards the first direction, the amplitude of each swing is 1 degree, the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope, the telescope is made to swing towards the second direction until the parallel distance between the telescope and the wall surface of the tunnel is increased, the amplitude of each swing is 30 degrees, and the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope; and circularly adjusting the sight line direction of the telescope in a reciprocating manner, changing the swinging direction of the telescope when the horizontal distance between the telescope and the wall surface of the tunnel is increased, and reducing the swinging amplitude of the telescope until the swinging amplitude of the telescope approaches to 0 infinitely, and acquiring the position with the minimum horizontal distance between the telescope and the wall surface of the tunnel.
Preferably, when the position pile number of the total station is determined through control point coordinate measurement, the position of the measuring station is recorded by using a measuring nail or paint spraying.
Preferably, the handheld laser device is a laser pen.
Preferably, the color of the laser light emitted by the hand-held laser device is different from the color of the laser light emitted by the total station.
Preferably, when the exposed traces on the same structural surface of the tunnel are connected end to end traces, the traces marked end to end are closed curves.
Preferably, the post-processing is performed on the exposed traces of all the structural surfaces, and the obtaining of the occurrence information of all the structural surfaces specifically includes:
note that the attitude of the structural plane is (α), wherein α is inclined and β is the inclination angle, there is
l＝sinβsinα (1a)
m＝sinβcosα (1b)
n＝cosβ (1c)
To obtain
β＝arccos(n) (2)
And (l, m and n) are normal vectors of planes of the same structural plane of the tunnel.
Preferably, when there are 3 feature points of the exposed trace line on the same structural surface of the tunnel, the normal vector of the plane where the same structural surface of the tunnel is located can be obtained according to the coordinates of the 3 feature points, and is marked as (l, m, n).
Preferably, when the number of feature points of the exposed traces on the same structural surface of the tunnel is more than 3, the method for performing plane equation fitting on the exposed traces on the same structural surface of the tunnel is a least square method.
Preferably, the calculation process of the least square method comprises the following steps:
setting the number of characteristic points of exposed traces of the same structural surface of the tunnel as N, wherein N is a positive integer greater than 3, converting the characteristic points into a global coordinate and recording the global coordinate as Pi(xi,yi,zi) At this time, the plane equation for the same structural plane of the tunnel is
Ax+By+Cz+D＝0 (3)
Wherein A, B, C and D are undetermined coefficients;
note feature point Pi(xi,yi,zi) Distance to plane diThe following are:
order to
For the objective function, L should be minimized, and the following requirements should be satisfied
Substituting the formula (2) into the formula (3) to obtain
Written in matrix form as follows
Determining coefficients A, B, C and D from equation (5);
from A, B, C and D, the normal vector of the structural surface can be determined as follows:
and if n is less than 0, inverting l, m and n simultaneously, wherein the normal vector of the plane of the same structural plane of the tunnel is marked as (l, m, n), namely the normal vector points to the upper half space.
The tunnel structure attitude double-laser collimation measuring method provided by the embodiment of the invention needs a prism-free total station to emit laser, can directly reflect light through an object to measure without installing reflecting equipment at a measuring point, and needs a reflecting facility, such as a prism or a reflector plate, to be installed at the measuring point for an ordinary total station without a prism-free function. The method is particularly suitable for double-laser collimation measurement of the shape of the structural plane of the tunnel constructed by a tunnel excavator method, can provide necessary basic information for searching key blocks of surrounding rocks of the tunnel and analyzing the stability of the surrounding rocks, and has important theoretical significance and engineering practical value.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings.
In the drawings:
fig. 1 is a flowchart illustrating steps of a double-laser collimation measurement method for tunnel structural plane attitude according to an embodiment of the present invention;
fig. 2 is a model diagram of a tunnel structural plane attitude double-laser collimation measurement method provided in the embodiment of the present invention in an application process.
Detailed Description
The invention provides a double-laser aiming measurement method for tunnel structural plane attitude, which aims to solve the problems in the prior art, can record the systematic structural plane of a tunnel formed by TBM excavation and acquire the attitude and trace network information of the structural plane, thereby providing necessary basic information for searching key blocks of tunnel surrounding rock and analyzing the stability of the surrounding rock, and being more practical.
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined objects, the following detailed description of the dual laser collimation measurement method for tunnel structural plane attitude according to the present invention, with reference to the accompanying drawings and preferred embodiments, describes specific embodiments, structures, features and effects thereof. In the following description, different "one embodiment" or "an embodiment" refers to not necessarily the same embodiment. Furthermore, the features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.
The term "and/or" herein is merely an association describing an associated object, meaning that three relationships may exist, e.g., a and/or B, with the specific understanding that: both a and B may be included, a may be present alone, or B may be present alone, and any of the three cases can be provided.
Referring to fig. 1 and fig. 2, the tunnel structural plane attitude double-laser collimation measuring method provided by the embodiment of the invention is realized under the condition of jointly applying a handheld laser device and a prism-free total station, and the measuring method comprises the following steps:
step S1: leveling the total station and adjusting a telescope arranged on the total station to enable the vertical angle reading of the telescope to be horizontal 0 degree;
step S2: adjusting the sight direction of the telescope, acquiring the position of the telescope with the minimum horizontal distance from the wall surface of the tunnel, defining the sight direction of the telescope as the direction vertical to the axis direction of the tunnel, and setting the horizontal azimuth angle of the sight direction of the telescope to be 0';
step S3: establishing a measuring coordinate system taking the axis direction of the tunnel as a Y axis and the zenith direction as a Z axis;
step S4: determining the position of the origin of the measurement coordinate system at the cross section of the tunnel according to the horizontal distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 0 degrees 0 ', the horizontal distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 180 degrees 0', and the diameter of the tunnel;
step S5: determining the position pile number of the total station through coordinate measurement of the control point, and simultaneously measuring the direction azimuth of the hole axis of the total station by using a geological compass to establish a survey station;
step S6: tracking the track of the tunnel structure surface by using a handheld laser device and confirming the characteristic points of the track of the tunnel structure surface;
step S7: rotating a lens of the total station, and locking the lens of the total station when a laser spot emitted by the total station is superposed with a laser spot emitted by the handheld laser device to obtain local coordinates of characteristic points of a track of a tunnel structure surface;
step S8: repeating the step of obtaining the local coordinates of the characteristic points of the tunnel structural surface trace until the number of the characteristic points reaches 3 or more, and connecting the characteristic points to obtain an exposed trace of the same structural surface of the tunnel, wherein at least 3 characteristic points are non-collinear characteristic points in the exposed trace of the same structural surface of the tunnel;
step S9: repeating the steps to obtain exposed traces of all structural surfaces within the effective measuring distance of the measuring station;
step S10: and carrying out post-processing on exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces.
The tunnel structure attitude double-laser collimation measuring method provided by the embodiment of the invention needs a prism-free total station to emit laser, can directly reflect light through an object to measure without installing reflecting equipment at a measuring point, and needs a reflecting facility, such as a prism or a reflector plate, to be installed at the measuring point for an ordinary total station without a prism-free function. The method is particularly suitable for double-laser collimation measurement of the shape of the structural plane of the tunnel constructed by a tunnel excavator method, can provide necessary basic information for searching key blocks of surrounding rocks of the tunnel and analyzing the stability of the surrounding rocks, and has important theoretical significance and engineering practical value.
The method for adjusting the sight direction of the telescope and acquiring the position with the minimum horizontal distance between the telescope and the wall surface of the tunnel comprises the following steps:
aiming the sight direction of the telescope at the wall surface of the tunnel, so that the sight of the telescope points to the axial direction perpendicular to the tunnel;
the telescope is swung left and right, the direction in which the horizontal distance between the telescope and the wall surface of the tunnel is reduced is recorded as a first direction, and the direction opposite to the first direction is recorded as a second direction;
the telescope is made to swing towards the first direction, the amplitude of each swing is 1 degree, the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope, the telescope is made to swing towards the second direction until the parallel distance between the telescope and the wall surface of the tunnel is increased, the amplitude of each swing is 30 degrees, and the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope; the sight direction of the telescope is adjusted in a reciprocating mode in a circulating mode, when the horizontal distance between the telescope and the wall surface of the tunnel is increased, the swinging direction of the telescope is changed, the swinging amplitude of the telescope is reduced, and the position with the minimum horizontal distance between the telescope and the wall surface of the tunnel is obtained until the swinging amplitude of the telescope approaches to 0 infinitely.
Through the mode, the telescope can be used for acquiring the position with the minimum horizontal distance from the telescope to the wall surface of the tunnel without adding other equipment, and the telescope is simple to operate and low in cost.
And when the position pile number of the total station is determined through the coordinate measurement of the control point, the position of the measuring station is recorded by using the measuring nail or the paint spraying. In this way the position of the station can be recorded very easily.
Wherein, the handheld laser device is a laser pen. The application cost is low.
The color of the laser emitted by the handheld laser device is different from that of the laser emitted by the total station. By the mode, the position of the laser spot emitted by the total station and the position of the laser spot emitted by the handheld laser device, which are superposed, can be conveniently confirmed.
When the exposed traces on the same structural surface of the tunnel are connected end to end, the traces marked with end to end connection are closed curves.
Wherein, post-processing the exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces specifically comprises:
note that the attitude of the structural plane is (α), wherein α is inclined and β is the inclination angle, there is
l＝sinβsinα (1a)
m＝sinβcosα (1b)
n＝cosβ (1c)
To obtain
β＝arccos(n) (2)
Wherein, (l, m, n) is a normal vector of a plane where the same structural plane of the tunnel is located.
When the number of the feature points of the exposed trace line for the same structural surface of the tunnel is 3, the normal vector of the plane where the same structural surface of the tunnel is located can be obtained according to the coordinates of the 3 feature points, and is marked as (l, m, n).
When the number of the feature points of the exposed traces on the same structural surface of the tunnel is more than 3, the method for performing plane equation fitting on the exposed traces on the same structural surface of the tunnel is a least square method.
The calculation process of the least square method comprises the following steps:
setting the number of characteristic points of exposed traces of the same structural surface of the tunnel as N, wherein N is a positive integer greater than 3, converting the characteristic points into a global coordinate and recording the global coordinate as Pi(xi,yi,zi) At this time, the plane equation for the same structural plane of the tunnel is
Ax+By+Cz+D＝0 (3)
Wherein A, B, C and D are undetermined coefficients;
note feature point Pi(xi,yi,zi) Distance to plane diThe following are:
order to
For the objective function, L should be minimized, and the following requirements should be satisfied
Substituting the formula (2) into the formula (3) to obtain
Written in matrix form as follows
Determining coefficients A, B, C and D from equation (5);
from A, B, C and D, the normal vector of the structural surface can be determined as follows:
and if n is less than 0, inverting l, m and n simultaneously, wherein the normal vector of the plane of the same structural plane of the tunnel is marked as (l, m, n), namely the normal vector points to the upper half space.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (9)
1. A double-laser collimation measurement method for tunnel structural plane attitude is characterized in that the measurement method is realized under the condition of jointly applying a handheld laser device and a prism-free total station, and comprises the following steps:
leveling the total station and adjusting a telescope disposed on the total station such that a vertical angle reading of the telescope is horizontal 0 °;
adjusting the sight direction of the telescope, acquiring the position of the telescope with the minimum horizontal distance from the wall surface of the tunnel, defining the sight direction of the telescope as the direction vertical to the axis direction of the tunnel, and setting the horizontal azimuth angle of the sight direction of the telescope to be 0';
establishing a measuring coordinate system taking the axis direction of the tunnel as a Y axis and the zenith direction as a Z axis;
determining the position of the origin of the measurement coordinate system at the cross section of the tunnel according to the parallel distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 0 degrees 0 ', the parallel distance between the total station and the wall surface of the tunnel when the horizontal azimuth angle is 180 degrees 0', and the diameter of the tunnel;
determining the position pile number of the total station through coordinate measurement of a control point, and simultaneously measuring the direction azimuth angle of the hole axis of the total station by using a geological compass to establish a survey station;
tracking the tunnel structure surface trace by using a handheld laser device and confirming the characteristic points of the tunnel structure surface trace;
rotating a lens of the total station, and locking the lens of the total station when a laser spot emitted by the total station is superposed with a laser spot emitted by the handheld laser device, so as to obtain local coordinates of characteristic points of the track of the tunnel structure surface;
repeating the step of obtaining the local coordinates of the feature points of the tunnel structural surface trace until the number of the feature points reaches 3 or more, and connecting the feature points to obtain an exposed trace of the same structural surface of the tunnel, wherein at least 3 feature points are non-collinear feature points in the exposed trace of the same structural surface of the tunnel;
repeating the steps to obtain exposed traces of all structural surfaces within the effective measuring distance of the measuring station;
carrying out post-processing on exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces; wherein the content of the first and second substances,
performing post-processing on the exposed traces of all the structural surfaces to obtain the occurrence information of all the structural surfaces, specifically:
note that the attitude of the structural plane is (α), wherein α is inclined and β is the inclination angle, there is
l＝sinβsinα (1a)
m＝sinβcosα (1b)
n＝cosβ (1c)
To obtain
β＝arccos(n) (2)
And (l, m and n) are normal vectors of planes of the same structural plane of the tunnel.
2. The dual laser sighting measuring method of tunnel structural surface attitude according to claim 1, wherein the method for adjusting the sight direction of the telescope to obtain the azimuth of minimum horizontal distance of the telescope from the wall surface of the tunnel comprises the following steps:
aiming the sight line direction of the telescope at the wall surface of the tunnel, so that the sight line of the telescope points to the axial direction perpendicular to the tunnel;
swinging the telescope left and right, recording the direction of the telescope, which is parallel to the wall surface of the tunnel, as a first direction, and recording the direction opposite to the first direction as a second direction;
the telescope is made to swing towards the first direction, the amplitude of each swing is 1 degree, the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope, the telescope is made to swing towards the second direction until the parallel distance between the telescope and the wall surface of the tunnel is increased, the amplitude of each swing is 30 degrees, and the parallel distance between the telescope and the wall surface of the tunnel is measured and recorded after each swing of the telescope; and circularly adjusting the sight line direction of the telescope in a reciprocating manner, changing the swinging direction of the telescope when the horizontal distance between the telescope and the wall surface of the tunnel is increased, and reducing the swinging amplitude of the telescope until the swinging amplitude of the telescope approaches to 0 infinitely, and acquiring the position with the minimum horizontal distance between the telescope and the wall surface of the tunnel.
3. The dual laser sighting method of tunnel structural face attitude of claim 1, wherein when determining the position pile number of said total station through control point coordinate measurement, the position of said station is recorded using a pin or paint.
4. The method for dual laser aiming measurement of tunnel structural face attitude according to claim 1, wherein the hand-held laser device is a laser pen.
5. The method of claim 1, wherein the color of the laser light emitted by the hand-held laser device is different from the color of the laser light emitted by the total station.
6. The method for measuring tunnel structural surface attitude by dual laser aiming according to claim 1, wherein when exposed traces of the same structural surface of the tunnel are end-to-end connected traces, the end-to-end connected traces are marked as a closed curve.
7. The method of claim 1, wherein when there are 3 feature points of the exposed trace lines on the same structural surface of the tunnel, the normal vector of the plane of the same structural surface of the tunnel is obtained according to the coordinates of the 3 feature points, and is marked as (l, m, n).
8. The method for measuring tunnel structural surface attitude by dual laser collimation according to claim 1, wherein when the number of feature points of the exposed trace of the same structural surface of the tunnel is more than 3, the method for performing plane equation fitting on the exposed trace of the same structural surface of the tunnel is a least square method.
9. The dual laser collimation measurement method for the tunnel structural plane attitude according to claim 8, wherein the calculation process of the least square method comprises the following steps:
setting the number of characteristic points of exposed traces of the same structural surface of the tunnel as N, wherein N is a positive integer greater than 3, converting the characteristic points into a global coordinate and recording the global coordinate as Pi(xi,yi,zi) At this time, the plane equation for the same structural plane of the tunnel is
Ax+By+Cz+D＝0 (3)
Wherein A, B, C and D are undetermined coefficients;
note feature point Pi(xi,yi,zi) Distance to plane diThe following are:
order to
For the objective function, L should be minimized, and the following requirements should be satisfied
Substituting the formula (2) into the formula (3) to obtain
Written in matrix form as follows
Determining coefficients A, B, C and D from equation (5);
from A, B, C and D, the normal vector of the structural surface can be determined as follows:
and if n is less than 0, inverting l, m and n simultaneously, wherein the normal vector of the plane of the same structural plane of the tunnel is marked as (l, m, n), namely the normal vector points to the upper half space.
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| CN113063397B (en) * | 2021-03-25 | 2022-12-06 | 北京市勘察设计研究院有限公司 | Tunnel cave wall joint structural plane attitude measuring method |
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| DE102005012107B4 (en) * | 2005-03-09 | 2010-04-29 | Angermeier Ingenieure Gmbh | Measuring system and method for geodetic surveying of objects |
| JP6611306B2 (en) * | 2015-04-15 | 2019-11-27 | 佐藤工業株式会社 | Tunnel management method |
| CN106289164A (en) * | 2016-08-06 | 2017-01-04 | 中国葛洲坝集团勘测设计有限公司 | A kind of cavern section method for fast measuring |
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