CN112257143B - Coordinate lattice tunnel blasting explosive quantity calculation method meeting multiple vibration speed requirements - Google Patents
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- 239000002360 explosive Substances 0.000 title claims abstract description 25
- 238000005422 blasting Methods 0.000 title claims abstract description 23
- 238000004364 calculation method Methods 0.000 title claims abstract description 13
- 238000000034 method Methods 0.000 claims abstract description 27
- 230000009466 transformation Effects 0.000 claims abstract description 15
- 239000003814 drug Substances 0.000 claims abstract description 12
- 238000004880 explosion Methods 0.000 claims description 6
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- 238000005553 drilling Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 2
- 229940079593 drug Drugs 0.000 abstract description 9
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F42—AMMUNITION; BLASTING
- F42D—BLASTING
- F42D1/00—Blasting methods or apparatus, e.g. loading or tamping
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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Abstract
The invention discloses a coordinate lattice tunnel blasting explosive quantity calculation method meeting the requirement of multiple vibration speeds, which is particularly suitable for carrying out tunnel blasting operation in a dense distribution area of protected building structures, and calculating the safe explosive quantity when the vibration speed control requirements of the building structures are different. Firstly, respectively establishing a plurality of independent space coordinate systems according to the linearity of a tunnel and the shape of a building structure; secondly, calculating the distances between points in different coordinate systems through coordinate transformation, finding out the shortest distance between a certain point on a tunnel and each protected building and the allowable value of the drug quantity, wherein the allowable value of the drug quantity calculated for different buildings meets the vibration speed control requirement; and finally, selecting the minimum value of each allowable dose value as the safe dose of the point on the tunnel, further obtaining the safe dose of each point in the whole tunnel process, and taking the safe dose as the reference value of the maximum single-section dose when each point of the tunnel is independently subjected to blasting operation. The invention has important significance for the fine design and construction of urban tunnel blasting.
Description
Technical Field
The invention provides a coordinate lattice tunnel blasting explosive quantity calculation method meeting the requirement of multiple vibration speeds, which is particularly suitable for calculating the tunnel blasting explosive quantity which meets the requirement of multiple vibration speeds when a plurality of structures are built nearby an urban tunnel and different vibration speed control requirements exist.
Background
In recent years, with the increase of urban tunnel projects, the workload of tunneling construction by using a drilling and blasting method is greatly increased. In tunneling construction, since blasting vibration affects safety of dense structures near a tunnel, attention should be paid to changes in spatial positional relationship between an excavated section and each structure at a time. Meanwhile, as vibration speed control requirements of different building structures are often different, along with continuous advancing of a working surface, the situation that the vibration speed allowable value of the building structure is high but is close to the working surface, the vibration speed allowable value is low but is far from a tunnel often occurs. Therefore, how to determine the blasting parameters (mainly the single-section maximum dosage) of the current working face according to the allowable vibration speed values of a plurality of building structures and the spatial position relation between the tunnel and the building structures in the tunneling process becomes a complex mathematical problem. At present, two main methods for solving the problem are: 1) Simplifying the building to one point, or directly taking the tunnel burial depth as the shortest distance from the tunnel to the building, can lead to inaccurate results; 2) The latest solving method based on geometry can be called as a profile line extension method, firstly, the projection intersection of the outer profile line of a building and a tunnel curve is required to be prolonged, and the tunnel is divided into a plurality of sections at the intersection point; secondly, listing equations describing the spatial distance relation for each segment of the tunnel; and finally, obtaining a safety dosage curve corresponding to each pile number of the tunnel. The disadvantage of this method is that: when a plurality of structures are built and the outer contour is irregular, the problems of too many tunnel sections and too complicated equations can occur, the results are inconvenient to obtain quickly, and even the solutions cannot be solved. The novel algorithm which is high in solving precision, high in solving speed, concise, easy to understand and capable of being popularized and used is needed to meet the requirement of fine blasting explosive quantity design of the urban tunnel.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a coordinate lattice tunnel blasting explosive quantity calculation method meeting the requirement of multiple vibration speeds.
The technical scheme adopted by the invention is as follows: firstly, respectively establishing a plurality of independent space coordinate systems according to tunnel linearity and building structure shape; secondly, calculating the distances between points in different coordinate systems through coordinate transformation, finding out the shortest distance between a certain point on a tunnel and each protected building and the allowable value of the drug quantity, wherein the allowable value of the drug quantity calculated for different buildings meets the vibration speed control requirement; and finally, selecting the minimum value of each allowable dose value as the safe dose of the point on the tunnel, further obtaining the safe dose of each point in the whole tunnel process, and taking the safe dose as the reference value of the maximum single-section dose when each point of the tunnel is independently subjected to blasting operation. The method specifically comprises the following steps:
(1) Establishing a tunnel association coordinate system and expressing a track equation:
the track curve of the tunnel explosion source is used for representing the trend of the tunnel in space, the track curve is formed by combining an arc curve section, a gentle curve section and a straight line section, and an independent coordinate system is respectively established for each line section to obtain a track equation of each line section under the corresponding coordinate system;
(2) Building a building associated coordinate system and expressing an outline:
the method comprises the steps that a plurality of protected buildings are arranged on the outer surface of a tunnel, an independent coordinate system is established for each building, dot matrix processing is carried out on all outer contour lines of each building, and a set of points capable of representing the outer contour of the building is obtained;
(3) Solving the shortest distance from any point of the tunnel to each building:
converting coordinate expression of a point on a track curve under a coordinate system corresponding to a line segment of the point into coordinates of the point under a certain building coordinate system through coordinate transformation, solving the distance from the point to all points in a point set representing the outer contour of the building, wherein the minimum value is the shortest distance from the point to the building, and sequentially solving the shortest distance from the point to each building in the same way;
(4) Solving the safety medicine value of each point of the tunnel under the requirement of multiple control vibration speeds:
substituting the shortest distance from a point on the track curve to one of the buildings and the allowable value of the vibration speed of the building into a known explosive quantity calculation formula to obtain an allowable value of the explosive quantity which meets the vibration speed control requirement of the building, sequentially solving the respective allowable value of the explosive quantity for all the buildings, comparing the sizes of all the allowable values of the explosive quantity, taking the minimum value as the safe explosive quantity of the point on the track curve which meets the vibration speed control requirement of all the buildings, representing the point by the pile number S information of the point, sequentially solving the safe explosive quantity Q of each point on the track curve, and making an S-Q curve;
(5) Selecting the maximum single-stage dosage in the blasting scheme:
when the tunnel is constructed to the pile number S by adopting a drilling and blasting method, the corresponding safe explosive quantity Q is selected according to the S-Q curve and is used as the maximum single-section explosive quantity in the blasting scheme.
The method considers the vibration speed control requirements of different building structures, and combines the S-Q curve to select the maximum single-section dosage of each point of the tunnel, so that the safety and the high efficiency of tunnel construction can be ensured. The safety is shown in that the safety dosage of each point of the tunnel is obtained through calculation, and the control requirement of each vibration speed is necessarily met; the high efficiency is shown that the actual dosage of each point of the tunnel is the maximum dosage under the condition that the vibration speed is required to be allowed, and the construction circulation footage is ensured. Compared with the prior art, the invention has the advantages that the geometric method is avoided to describe the outline of the conventional or special-shaped building structure, and meanwhile, the coordinate transformation of the space rectangular coordinate system is utilized to effectively avoid the prior need of listing complex space distance equations. The method has better inclusion for the special-shaped building structures, and does not limit the number of the protected building structures.
Drawings
FIG. 1 is a tunnel and building coordinate system establishment
FIG. 2 is a detail of a building outline
FIG. 3 is a schematic view of the position of the point N
FIG. 4 is a schematic diagram of a coordinate transformation process
FIG. 5 shows the pile number versus the drug quantity (S-Q) i ) Curve of curve
FIG. 6 is a pile number-drug quantity (S-Q) curve for simultaneously satisfying 3 vibration velocity requirements
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the specific embodiments and with reference to the accompanying drawings.
The process supported by the invention is a Guanyin bridge tunnel in the North China of Chongqing city, and the method of the invention is now described in detail according to the whole-course blasting medicine amount calculation of the Guanyin bridge tunnel, but the invention is not limited to the implementation case.
The guanyin bridge tunnel is positioned in the Jiangbei area of Chongqing city, the curve characteristics and the key protected building distribution area are considered, the tunnel ZK1+ 159.560-ZK1+ 386.759 sections are taken for calculation, as shown in figure 1, the section is divided into a moderating curve section 1, a circular curve section and a moderating curve section 2 in a linear mode, namely ZK1+ 159.560-219.560 is the moderating curve section 1, ZK1+326.759-386.759 is the moderating curve section 2, and the middle part ZK1+ 219.560-326.759 is the circular curve section. The key protection structure is arranged outside the outline of the tunnel: chongqing municipal design institute, fubi district and northern city perch, the allowable value of blasting vibration is different: vibration speed tolerance value at municipal design institute [ v ] A ]＝0.5cm·s -1 The method comprises the steps of carrying out a first treatment on the surface of the Safe vibration speed tolerance value [ v ] at northern city perch B ]＝1.0cm·s -1 The method comprises the steps of carrying out a first treatment on the surface of the Safe vibration speed tolerance value [ v ] at Fubi district C ]＝1.0cm·s -1 . The specific implementation steps are as follows:
(1) Establishment of a tunnel coordinate system and expression of an equation:
the relaxation curve is used for connecting straight line segmentsThe connection point of the circular curve section and the straight line section is called a straight slow point, and the connection point of the circular curve section and the straight line section is called a slow dot. The tunnel is taken from the straight and slow point 1 (the intersection point of the gentle curve section 1 and the straight line section), and the pile number S zh1 ZK1+159.560, up to the straight and slow point 2, pile number S zh2 Zk1+386.759. Pile number S of slow round point 1 (intersection point of slow curve segment 1 and circular curve segment) hy1 Is ZK1+219.560, the dots are slowly and slowly arranged with the pile number of 2S hy2 Zk1+326.759. The tunnel-related parameters are: radius of circle curve segment r=100deg.M, length of two-segment moderation curve s 1 ＝s 2 The longitudinal slope gradient i= ±4 m, the curve is advanced to the large mileage, the curve is advanced to the small mileage, the curve is negatively, the pile number of the tunnel slope change point is ZK1+119.560, and the tunnel section i is positive. All the coordinate system origins O and the straight slow points 1 are at the same elevation, and the altitude is 257.2m.
1) Moderating curve segment coordinate system establishment and equation expression
For the moderating curve segment 1, its coordinate system O 1 X 1 Y 1 Z 1 Origin O 1 The altitude of the (A) is consistent with the altitude of the straight slow point 1, coincides with the vertical projection of the slow point 1, and Z is 1 The axis passes through the slow round dots 1, Y vertically upwards 1 X is arranged on one side of the curvature center of the axial back-to-back moderation curve 1 The axes are established according to a cartesian coordinate system.
Setting any point in the curve as S 1 The equation for the mild curve segment 1 is expressed as:
in (x) 1 ,y 1 ,z 1 ) Is the pile number S in the curve 1 Is at the point O 1 X 1 Y 1 Z 1 The coordinates below.
Similarly, for the mild curve segment 2, its coordinate system O 2 X 2 Y 2 Z 2 Origin O 2 Is consistent with the altitude of the straight slow point 1, coincides with the vertical projection of the straight slow point 2, and Z 2 The axis passing vertically upwards through the straight and slow point 2, Y 2 The axis points to the side of the curvature of the gentle curve, X 2 The axes are established according to a cartesian coordinate system.
Let the pile number at any point in the curve be S 2 The equation for the mild curve segment 2 is expressed as:
in (x) 2 ,y 2 ,z 2 ) Is the pile number S in the curve 2 Is at the point O 2 X 2 Y 2 Z 2 The coordinates below.
2) Establishing a coordinate system of a circular curve segment and expressing a coordinate system O of the circular curve segment by using an equation 3 X 3 Y 3 Z 3 Origin O 3 Is consistent with the altitude of the straight slow point 1, and the origin point O 3 Is coincident with the center of the circle curve segment, Z 3 The axis is directed directly above X 3 Vertical projection of the axis through the dots 1, Y 3 The axes are established according to a cartesian coordinate system.
Set X 3 The pile number of the intersection point of the shaft and the tunnel curve is S 0 Pile number S at any point on tunnel curve 3 The equation for the circular curve segment is expressed as:
in (x) 3 ,y 3 ,z 3 ) Is the pile number S in the curve 3 Is at the point O 3 X 3 Y 3 Z 3 The coordinates below.
(2) Building a building coordinate system and expressing points:
the coordinate system of each building is shown in FIG. 1, and the municipal institute marks building A and the coordinate system is O A X A Y A Z A The method comprises the steps of carrying out a first treatment on the surface of the The northern city perch district is marked as a building B, and the coordinate system is O B X B Y B Z B The method comprises the steps of carrying out a first treatment on the surface of the The Fubi district is marked as a building C, and the coordinate system is O C X C Y C Z C . The building outline is shown in detail in fig. 2. The outline of A is formed by enclosing six straight line sections of A1, A2, A3, A4, A5 and A6; the outline of B is formed by enclosing six straight line sections of B1, B2, B3, B4, B5 and B6; the outline of C is formed by enclosing six straight line sections of C1, C2, C3, C4, C5 and C6. Because the bottom layer of the building is closest to the underground explosion source than other layers, the shortest distance in the calculation of the safe dosage can only be generated by connecting the explosion source with a certain point in the outline of the building base, and the outline of the building base is lattice-typed for the convenience of calculation.
The elevation of the substrate of A is 285.7m, the altitude of the straight and slow point 1 is 257.2m, and the vertical coordinate z A =28.5m, the set of points on the contour is T A ＝T A1 ∪T A2 ∪……∪T A6 Wherein T is A1 、T A2 ……T A6 The point sets for each edge on the contour line are respectively as follows:
similarly, the elevation of the substrate of B is 298.3m, z B =41.1m, the set of points on the contour is T B ＝T B1 ∪T B2 ∪……∪T B6 Wherein T is B1 、T B2 ……T B6 The points are respectively point sets of each side on the contour line of the northern city perch, and the point sets are represented by the following formula:
c substrate elevation 302.9m, z C =45.7m, the set of points on the contour is T C ＝T C1 ∪T C2 ∪……∪T C6 Wherein T is C1 、T C2 ……T C6 The points on each side of the contour line of the Fubi cell are respectively as follows:
(3) Determination of the shortest distance from the tunnel point to each building:
taking building A as an example, A has a coordinate system of O A X A Y A Z A As shown in FIG. 3, the mild curve segment 2 has a point N at O 3 X 3 Y 3 Z 3 The lower coordinates are (x 3 ,y 3 ,z 3 ) If the two are not in the same coordinate system, if the shortest distance from the point N to the point A is required to be resolved, the point N is obtained by coordinate transformation A X A Y A Z A Lower coordinates (x 3A ,y 3A ,z 3A ). Since the Z-axes of all coordinate systems are co-directional and the origin is in the same horizontal plane, all coordinate system transformations herein are essentially planar coordinate system transformations around the Z-axis (after coordinate transformation, the Z-value is unchanged). As shown in FIG. 4, the coordinate system O 3 X 3 Y 3 Z 3 Conversion to O A X A Y A Z A Two transformations are needed, the first transformation being the coordinate system O 3 X 3 Y 3 Z 3 Rotate theta around Z axis to coordinate system O 3 ’X 3 ’Y 3 ’Z 3 ' θ is Y 3 And Y is equal to A The angle of the axes is shown as:
the second transformation being the coordinate system O 3 ’X 3 ’Y 3 ’Z 3 ' along X 3 ' move a distance a along axis Y 3 ' distance of shaft movement b to O A X A Y A Z A As shown in the formula:
each Z-axis is out of the plane of the drawing. For the simple calculation of MATLAB, the rotation transformation and translation transformation expressed by the two formulas are uniformly expressed as a reversible 4×4 square matrix as shown in the formulas:
can be set at point N at O 3 X 3 Y 3 Z 3 Lower coordinates (x 3 ,y 3 ,z 3 ) Conversion to O A X A Y A Z A Lower coordinates (x 3A ,y 3A ,z 3A ). The 4 th element 1 in the column vector has no physical meaning, and is only used for expanding the rank of the vector to 4 so as to perform matrix operation.
Point N to A outline Point set T A Any point in the interior (x) A ,y A ,z A ) The distance of (2) is:
sequentially calculating point N to A outline point set T by using MATLAB software for loop sentence A The distance between all points in the range is taken as the minimum value of the distance R between the points N and A NA The shortest distance R from the point N to B, C can be obtained by the same method NB 、R NC . (4) determination of safe dosage under multi-control vibration speed:
r is R NA Substituting into any one R, Q, v single relation to obtain the allowable value [ v ] of the A vibration speed at the point N A ]Safety dosage Q under requirement NA The invention takes a Sachs formula as an example:
wherein R is NA Is the space distance from the explosion source point N to the building A, v A Is the control vibration speed of the building A, Q NA At vibration velocity v A The safety dosage of the lower point N is required, and K and alpha are parameters related to the explosion source and site conditions.
The allowable value v of the vibration velocity of the point N in the building B, C can be obtained by the same method C ]、[v B ]Safety dosage Q under requirement NB 、Q NC As shown in FIG. 5, Q NB ＜Q NC ＜Q NA So choose Q NB Is the safe drug amount of point N. Similarly, the MATLAB software can be used to obtain safe drug amounts meeting 3 vibration speed tolerance values at each point on the tunnel, and the result is input into Origin software to make a S-Q (pile number-safe drug amount) curve of the tunnel as shown in figure 6.
The above is an embodiment of the present invention, and the method is equally applicable to other formulas for calculating the dosage by distance and vibration velocity control. According to several of the main features listed above, all of these features are met and should be considered as the same type of the present invention.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (1)
1. A method for calculating the blasting explosive quantity of a coordinate lattice tunnel meeting the requirement of multiple vibration speeds is characterized by comprising the following steps:
(1) Establishing a tunnel association coordinate system and expressing a track equation:
the track curve of the tunnel explosion source is used for representing the trend of the tunnel in space, the track curve is formed by combining an arc curve section, a gentle curve section and a straight line section, and an independent coordinate system is respectively established for each line section to obtain a track equation of each line section under the corresponding coordinate system;
(2) Building a building associated coordinate system and expressing an outline:
the method comprises the steps that a plurality of protected buildings are arranged on the outer surface of a tunnel, an independent coordinate system is established for each building, dot matrix processing is carried out on all outer contour lines of each building, and a set of points capable of representing the outer contour of the building is obtained;
(3) Solving the shortest distance from any point of the tunnel to each building:
converting coordinate expression of a point on a track curve under a coordinate system corresponding to a line segment of the point into coordinates of the point under a certain building coordinate system through coordinate transformation, solving the distance from the point to all points in a point set representing the outer contour of the building, wherein the minimum value is the shortest distance from the point to the building, and sequentially solving the shortest distance from the point to each building in the same way;
(4) Solving the safety medicine value of each point of the tunnel under the requirement of multiple control vibration speeds:
substituting the shortest distance from a point on the track curve to one of the buildings and the allowable value of the vibration speed of the building into a known explosive quantity calculation formula to obtain an allowable value of the explosive quantity which meets the vibration speed control requirement of the building, sequentially solving the respective allowable value of the explosive quantity for all the buildings, comparing the sizes of all the allowable values of the explosive quantity, taking the minimum value as the safe explosive quantity of the point on the track curve which meets the vibration speed control requirement of all the buildings, representing the point by the pile number S information of the point, sequentially solving the safe explosive quantity Q of each point on the track curve, and making an S-Q curve;
(5) Selecting the maximum single-stage dosage in the blasting scheme:
when the tunnel is constructed to the pile number S by adopting a drilling and blasting method, the corresponding safe explosive quantity Q is selected according to the S-Q curve and is used as the maximum single-section explosive quantity in the blasting scheme.
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