CN111751872A - System and method for predicting blasting vibration speed of central area of side wall of underground cavern - Google Patents
System and method for predicting blasting vibration speed of central area of side wall of underground cavern Download PDFInfo
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Abstract
The invention discloses a system and a method for predicting blasting vibration speed of a central area of a side wall of an underground cavern, wherein the system comprises a plurality of vibration speed sensors, a plurality of vibration speed sensors and a plurality of sensors, wherein the plurality of vibration speed sensors are arranged on the side wall of a first underground cavern and are used for detecting the vibration speed generated by blasting, and the distances between the plurality of vibration speed sensors and the first blasting point generating blasting and two vertical edges of the side wall of the first underground cavern are both larger than a preset value; and the processing module is used for fitting a preset model based on an output signal of the vibration speed sensor in the training mode to obtain a prediction model, and predicting the blasting vibration speed of the predicted point through the prediction model in the prediction mode to obtain a prediction result. The method can utilize the cannon test to rapidly model different underground cavern side walls and predict the blasting vibration speed of the same type of underground cavern side walls according to the prediction model. The invention can be widely applied to blasting auxiliary technology.
Description
Technical Field
The invention relates to a blasting auxiliary technology, in particular to a system and a method for predicting blasting vibration speed of a central area of a side wall of an underground cavern.
Background
At present, the blast excavation construction method of rock mass is still the main project of the excavation of underground powerhouse, underground nuclear waste storage warehouse, underground petroleum cave depot, underground military project, underground mine exploitation and the like of hydropower station. The Peak Particle vibration Velocity (PPV) of the side wall induced by blasting excavation of the underground cavern is a key index for controlling damage of the side wall surrounding rock.
At present, the blast vibration speed is mainly predicted based on the Sudofski prediction formula, but the Sudofski prediction formula is only suitable for predicting the PPV of the flat ground. Different terrain structures have different model parameters, but the prior art is difficult to carry out rapid modeling and blast vibration speed prediction aiming at different target environments.
Disclosure of Invention
To solve at least one of the above-mentioned technical problems, the present invention is directed to: a system and a method for predicting blasting vibration speed of a central area of a side wall of an underground cavern are provided, so that rapid modeling and blasting vibration speed prediction can be performed on different side walls of the underground cavern.
In a first aspect, an embodiment of the present invention provides:
a system for predicting blasting vibration speed of a central area of a side wall of an underground cavern comprises:
the system comprises a plurality of vibration speed sensors, a first underground cavern side wall and a second underground cavern side wall, wherein the plurality of vibration speed sensors are arranged on the first underground cavern side wall and are used for detecting the vibration speed generated by blasting, and the distances between the plurality of vibration speed sensors and the first blasting point generating blasting and two vertical sides of the first underground cavern side wall are larger than a preset value;
a processing module to:
in a training mode, receiving first configuration parameters, wherein the first configuration parameters comprise coordinates of a plurality of vibration sensors in a first coordinate system, the length and the height of a side wall of the first underground cavern, the distance between the plurality of vibration sensors and a first explosion point and a first explosive amount, responding to a starting signal, receiving output signals of a plurality of vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the plurality of vibration sensors and the first configuration parameters to obtain a prediction model;
receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of a prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, a second explosive quantity, and the length and the height of a side wall of a second underground cavern where the second explosion point is located, and substituting the second configuration parameters into the prediction model to obtain the vibration speed of the prediction point;
the first coordinate system is a coordinate system established by taking the set top angle of the first underground cavern side wall as an origin, and the second coordinate system is a coordinate system established by taking the set top angle of the second underground cavern side wall as the origin.
Further, the preset value is greater than 1/3 of the transverse length of the side wall of the first underground cavern.
Further, the prediction model is:
wherein V represents the vibration speed of the prediction point, (x, y) represents the coordinate of the prediction point, a represents the length of the underground cavern side wall where the explosion point is located, b represents the height of the underground cavern side wall where the explosion point is located, k, β1And β2Q is the explosive amount and R is the distance between the predicted point and the explosion point.
Further, the parameter fitting is performed on a preset model based on the output signals of the plurality of vibration sensors and the first configuration parameter to obtain a prediction model, specifically:
using the output signals of the plurality of vibration sensors as V, and performing parameter fitting on a prediction model by combining first configuration parameters to obtain k and β1And β2Thereby obtaining a prediction model.
Further, the prediction model satisfies the following constraint relationship:
further, the distribution positions of the plurality of vibration speed sensors are located on the same straight line.
Further, a plurality of the vibration speed sensors are equidistantly distributed.
Further, the plurality of vibration speed sensors are connected with the processing module in a wireless mode.
In a second aspect, an embodiment of the present invention provides:
a method for predicting blasting vibration speed of a central area of a side wall of an underground cavern is applied to a processing module in the system, and is characterized by comprising the following steps:
determining a mode;
receiving first configuration parameters in a training mode, wherein the first configuration parameters comprise coordinates of the vibration sensors in a first coordinate system, the length and the height of the side wall of the first underground cavern, the distance between the vibration sensors and a first explosion point and a first explosive amount;
responding to a starting signal, receiving output signals of the vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the vibration speed sensors and the first configuration parameter to obtain a prediction model;
receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of a prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, the second explosive quantity, and the length and the height of a second underground cavern side wall where the second explosion point is located;
and substituting the second configuration parameter into the prediction model to obtain the vibration speed of the predicted point.
Further, the prediction model is:
wherein V represents the vibration speed of the prediction point, (x, y) represents the coordinate of the prediction point, a represents the length of the underground cavern side wall where the explosion point is located, b represents the height of the underground cavern side wall where the explosion point is located, k, β1And β2Q is the explosive amount and R is the distance between the predicted point and the explosion point.
The embodiment of the invention has the beneficial effects that: the method combines a model related to the coordinates of the vibration sensor in a first coordinate system, the length and the height of the first underground cavern side wall, the distance between the vibration sensor and a first explosion point and the first explosive quantity, and fits the model based on data collected by the vibration sensor in a training mode, so that a prediction model applied in the prediction mode is obtained, a small shot test can be used for quickly modeling different underground cavern side walls, and the explosion vibration speed of the same type of underground cavern side walls is predicted according to the prediction model.
Drawings
FIG. 1 is a schematic diagram illustrating an installation manner of a system for predicting blasting vibration velocity of a central area of a side wall of an underground cavern according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a mechanical model provided in accordance with an embodiment of the present invention;
FIG. 3 is a first mode shape diagram of the model of FIG. 2;
fig. 4 is a schematic view of another installation manner of a blasting vibration speed prediction system for a central area of a side wall of an underground cavern according to an embodiment of the invention.
Detailed Description
The invention is further described with reference to the drawings and the specific examples.
With the deep knowledge of the propagation law of the earthquake waves of the blasting by the inventor, the fact that the actual measurement value of the PPV of the blasting of engineering objects such as side slopes, underground cavern side walls and the like does not change in a power exponential function along with the distance of the blasting source, but the predicted value of the Pisato-fusi formula is much larger, and an obvious amplification effect exists. The inadaptability of the traditional Sadawski formula to the PPV response of the side wall surrounding rock is continuously highlighted, so that special research is urgently needed for predicting the blasting vibration speed of the underground cavern.
Wherein, the traditional sarofsky formula is:
k is a coefficient considering geological influence and topographic influence; alpha is the blasting seismic wave attenuation coefficient of the blasting seismic wave related to the geological condition and the geological condition; q is the maximum single dose; and R is the distance between the measuring point and the explosion source.
Referring to fig. 1, in order to solve the problem that the related art cannot be quickly modeled and cannot accurately predict, the embodiment provides a system for predicting blasting vibration velocity of a central area of a side wall of an underground cavern, which includes:
and a plurality of vibration speed sensors 110 disposed on the first underground cavern side wall 120 for detecting vibration speed generated by the explosion, wherein distances between the plurality of vibration speed sensors and the first explosion point 130 generating the explosion and the vertical sides 140a and 140b of the first underground cavern side wall 120 are greater than a preset value, and fig. 1 includes a vault 150a, a vault line 150b and a bottom plate 150 c.
A processing module to:
in a training mode, receiving first configuration parameters, wherein the first configuration parameters comprise coordinates (x, y) of a plurality of vibration sensors in a first coordinate system, the length a and the height b of a side wall of the first underground cavern, the distance R between the plurality of vibration sensors and a first explosion point and a first explosive quantity Q, responding to a starting signal, receiving output signals of the plurality of vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the plurality of vibration sensors and the first configuration parameters to obtain a prediction model;
receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of a prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, a second explosive quantity, and the length and the height of a side wall of a second underground cavern where the second explosion point is located, and substituting the second configuration parameters into the prediction model to obtain the vibration speed of the prediction point;
the first coordinate system is a coordinate system established by taking the set top angle of the first underground cavern side wall as an origin, and the second coordinate system is a coordinate system established by taking the set top angle of the second underground cavern side wall as the origin. As shown, the coordinates may have the lower left vertex of the wall as the origin.
The processing module includes an input device and a display device for providing a configuration interface, and the initiation signal may be a signal indicating that the device is ready, which may be associated with a signal triggering a burst.
Wherein, the prediction model is as follows:
wherein V represents the vibration speed of the prediction point, (x, y) represents the coordinate of the prediction point, and a represents the length of the side wall of the underground cavern where the explosion point is positionedDegree, b represents the height of the side wall of the underground cavern where the explosion point is located, k, β1And β2Q is the explosive amount and R is the distance between the predicted point and the explosion point.
It is to be understood that the difference between the pre-set model and the predictive model is the fitting parameters k, β1And β2Difference in value β1For blast seismic wave attenuation coefficient associated with geological conditions, β2And k is a coefficient of geological influence, side wall four-side constraint and terrain influence. The establishing process of the prediction model is as follows:
compared with a semi-infinite space, the propagation of a natural earthquake is influenced by a cavity effect and a terrain effect of an underground cavern, namely, the vibration waves can generate complex reflection and diffraction effects on the surface of surrounding rocks of the cavern, so that the central area of a side wall is changed into a stress relaxation area, and an obvious PPV amplification effect is shown.
When the problem of high-rise building vibration caused by ground vibration is generally considered, a mode analysis method is often used for determining vibration response modes under different frequencies. The continuous body of the surrounding rock is abstracted into a plurality of rock strata, the surrounding rock on the surface layer of the side wall is abstracted into thin plates with equal thickness, and elastic connection is arranged between the surrounding rock on the deep layer and the surrounding rock on the surface layer. The upper end and the lower end of the surface layer surrounding rock of the side wall of the underground cavern are respectively provided with the top plate and the bottom plate, and the left end and the right end of the surface layer surrounding rock are respectively provided with the constraint action of the boundary, so that the underground cavern side wall has the characteristic of a typical four-side simple support plate, is different from a common four-side simple support plate, and is subjected to preliminary analysis by using the simplified conditions. The total length of the cavern is equivalent to the total length a of the plate, and the total height of the cavern is equivalent to the total width b of the plate. The simplified mechanical model and the corresponding mode diagram are shown in fig. 2 and fig. 3.
This application has simplified the side direction atress condition of four sides constraint condition and top layer country rock, because the source of explosion position is near the side wall bottom, so with the blasting load equivalence for being used in arbitrary one point (x, y) department on the four sides simple-supported board and act on a simple harmonic concentrated load F (x, y, t), the forced vibration equation of four sides simple-supported sheet metal is:
in the case of a blast impact load, irrespective of the damping effect of the system, it can be assumed that in equation (1)
F(x,y,t)＝q(x,y)sinωt
w(x,y,t)＝w(x,y)sinωt
The vibration differential equation becomes
In formula (2): w is the displacement of the coordinate axis in the z direction,
is the mass per unit area of the sheet, D is the bending stiffness of the sheet,
e, mu are the elastic modulus and Poisson coefficient of the material, q (x, y) is the disturbance force amplitude, and w (x, y) is the deflection surface amplitude equation.
The method is characterized in that a simple harmonic transverse unit concentrated load acts on any point (zeta, eta) on the four-side simple support plate, and a basic solution of the power of a deflection surface equation of the four-side simple support rectangular plate can be obtained:
in the formula (I), the compound is shown in the specification,
the bending surface equation when the force F (t) applied to the four-side simple plate at any position (ζ, η) is not unit simple harmonic force is solved by the basic solution of the dynamic force:
partial differentiation is carried out on the time t by the above formula, and the vibration speed of any point on the plate at any moment is obtained as follows:
in general, for more rigid rock-soil structures such as high slopes, underground caverns, only the first order mode-shape problem is considered, and for each blast, the point of application of the load (ζ, η) is a known point (i.e.,
known quantity), the ratio of the PPV at any point on the board to the maximum velocity peak value on the whole board can be calculated to be sin (m pi x/a) sin (n pi y/b), and the value can be used as a dimensionless quantity for representing the characteristic of the ratio of the PPV at any measuring point of the side wall to the maximum velocity peak value on the whole side wall.
The method comprises the following steps of (1) side wall vibration PPV dimension analysis considering the four-side constraint effect:
according to the result of the dynamics analysis, the PPV of any measuring point on the surface of the blasting side wall of the underground cavern is related to a sine function of a measuring point abscissa x, a cavern total length a, a measuring point ordinate y, a side wall total height b and x/a and y/b. In addition, according to the response analysis of the traditional blasting vibration problem, the blasting vibration is mainly subjected to landform, geological conditions, measuring point blasting center distance R, surface rock mass point vibration displacement mu and surface rock mass point vibration acceleration
The natural vibration frequency f of the rock mass, the maximum single-response drug quantity Q, the rock mass density rho, the propagation speed c of the vibration wave and the detonation time t. Through dimensional analysis, the PPV of the blasting side wall of the underground cavern can be expressed as:
as can be seen from the number of parameters, the total analysis number of the physical quantity is 10, and the independent variable (Q, R, c) is taken according to the pi theorem, so that 7 pi components exist, and pi is used asiRepresenting a dimensionless quantity, then:
the substitution of formula (2) for formula (1) is,
in addition, a dimensionless quantity can be obtained,
since ρ and c are approximately constant under the same site conditions, V and c can be found from equation (11)
Having a functional relationship, the function can then be written as:
wherein the content of the first and second substances,
what the term characterizes is the effect of the sidewall quadrilateral constraint on the PPV. If the term is not considered, then the Sudofski equation can be solved:
if the influence of the side wall four-edge constraint on the PPV is considered, the method can be obtained by solving the following equation (12):
order to
Then there are:
in the formula α1、α2K is a coefficient considering geological influence, side wall four-side constraint and terrain influence, β1PPV damping coefficient for blasting vibration related to geological conditions β2And (5) restraining influence factors for four sides of the side wall.
The application of the formula is the same as the blast vibration prediction empirical formula mentioned above, the blast test is carried out on site, regression analysis is carried out by measuring the distance between the blast centers, the horizontal distance between the blast centers, the total length of the cavern, the vertical distance between the blast centers, the total height of the cavern, the explosive quantity and the PPV measured value, and the coefficients k and β are determined1、β2Thereby obtaining the blasting vibration prediction formula of the form (15).
In some embodiments, the predetermined value is greater than 1/3 for the lateral length of the first underground cavern side wall.
In some embodiments, the processing module may also be based on parameters k, β in the predictive model1And β2And calculating the maximum single-response explosive quantity. The calculation method is as follows:
wherein, based on the maximum allowable V value of the prediction point, the maximum single-response explosive quantity Q can be calculated. Thus, engineering blasting can be guided.
In some embodiments, the performing parameter fitting on a preset model based on the output signals of the plurality of vibration sensors and the first configuration parameter to obtain a prediction model specifically includes:
using the output signals of the plurality of vibration sensors as V, and performing parameter fitting on a prediction model by combining first configuration parameters to obtain β1And β2Thereby obtaining a prediction model.
In some embodiments, the predictive model satisfies the following constraint relationship:
In some embodiments, the distribution positions of the plurality of vibration speed sensors are located on the same straight line. The vibration speed sensors are distributed at equal intervals. The sensor arrangement mode of the embodiment enables data to have a relatively obvious rule, so that model fitting is facilitated, and the time for model fitting is favorably shortened.
In some embodiments, the plurality of vibration speed sensors and the processing module are connected wirelessly. The embodiment is connected in a wireless mode, so that remote testing can be realized, and the situation that cave collapse and the like cause that the processing module cannot be taken out is avoided.
This example discloses experimental procedures and data of examples of the present application.
Referring to fig. 4, the size of the dead zone of the underground cavern is 10m × 32m × 12m, the blasting holes are positioned on the surface of the side wall and drilled perpendicular to the side wall, 2 times of blasting is carried out in the test and respectively completed in the No. I blasting holes 412 and the No. II blasting holes 422, the blasting holes are positioned on the surface of the side wall, the hole diameter is 38mm, the hole depth is 2m, and the method adopts
The emulsion explosive is continuously charged, the maximum single explosive quantity is 4kg, and the coordinates of No. I and No. II blast holes are (15,1) and (25,1) respectively in figure 4, which is shown in figure 4.
As shown in FIG. 4, in each blasting, 8 measuring points are vertically arranged on the surface of the side wall from bottom to top, and the distance between every two adjacent measuring points is 1 m. The measuring points with the relative height of 3 m-10 m are named as Mp 1-Mp 8 and Mp 9-Mp 16 in sequence.
Wherein, the maximum single-sound dose Q, the total length a of the side wall of the underground cavern, the total height b of the side wall of the underground cavern, the distance R between a measuring point and an explosion source, and the speed peak of explosion vibrationValue V, calculating unknown coefficients k, β in the prediction formula by a binary linear regression analysis method1、β2The method comprises the following specific steps:
first of all a calculation is made lnV of,
and
then the value of (c) is compared to lnV,
and
performing binary linear regression analysis on the values to obtain the intercept and the slope of a linear equation, and obtaining unknown coefficients k being 53.06 and β in the formula by adopting an exponential function with a low natural constant e1＝0.75，β21.11, thereby obtaining the concrete form of the underground cavern side wall blasting vibration prediction formula
And substituting parameters such as single-shot dose, shot center distance, height difference and the like corresponding to the data of each measuring point into a prediction formula to obtain a blasting vibration prediction value of each measuring point. Representative data, namely data of the near zone of the explosion source and the central area of the side wall are selected for verification and comparison, and are shown in table 1. The table shows that the prediction accuracy of the PPV measured point on the blasting side wall of the underground cavern is higher by considering the blasting vibration prediction formula of the constraint influence of the four side ends of the side wall.
TABLE 1
The embodiment discloses a method for predicting blasting vibration speed of a central area of a side wall of an underground cavern, which is applied to a processing module in the system and is characterized by comprising the following steps of:
s201, determining a mode; specifically, a mode selection interface is displayed to the user, and the mode is determined in response to an operation instruction for the selection interface.
S202, receiving first configuration parameters in a training mode, wherein the first configuration parameters comprise coordinates of the vibration sensors in a first coordinate system, the length and the height of the side wall of the first underground cavern, the distance between the vibration sensors and a first explosion point and a first explosive amount;
s203, responding to a starting signal, receiving output signals of the plurality of vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the plurality of vibration speed sensors and the first configuration parameter to obtain a prediction model;
s204, receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of the prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, a second explosive quantity, and the length and the height of a second underground cavern side wall where the second explosion point is located;
and S205, substituting the second configuration parameter into the prediction model to obtain the vibration speed of the predicted point.
The step numbers in the above method embodiments are set for convenience of illustration only, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A system for predicting blasting vibration velocity of a central area of a side wall of an underground cavern, which is characterized by comprising:
the system comprises a plurality of vibration speed sensors, a first underground cavern side wall and a second underground cavern side wall, wherein the plurality of vibration speed sensors are arranged on the first underground cavern side wall and are used for detecting the vibration speed generated by blasting, and the distances between the plurality of vibration speed sensors and the first blasting point generating blasting and two vertical sides of the first underground cavern side wall are larger than a preset value;
a processing module to:
in a training mode, receiving first configuration parameters, wherein the first configuration parameters comprise coordinates of a plurality of vibration sensors in a first coordinate system, the length and the height of a side wall of the first underground cavern, the distance between the plurality of vibration sensors and a first explosion point and a first explosive amount, responding to a starting signal, receiving output signals of a plurality of vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the plurality of vibration sensors and the first configuration parameters to obtain a prediction model;
receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of a prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, a second explosive quantity, and the length and the height of a side wall of a second underground cavern where the second explosion point is located, and substituting the second configuration parameters into the prediction model to obtain the vibration speed of the prediction point;
the first coordinate system is a coordinate system established by taking the set top angle of the first underground cavern side wall as an origin, and the second coordinate system is a coordinate system established by taking the set top angle of the second underground cavern side wall as the origin.
2. The system of claim 1, wherein the predetermined value is greater than 1/3 times the length of the first underground cavern side wall.
3. The system for predicting blasting vibration velocity of the central area of the side wall of the underground cavern as claimed in claim 1, wherein the prediction model is as follows:
wherein V represents the vibration speed of the prediction point, (x, y) represents the coordinate of the prediction point, a represents the length of the underground cavern side wall where the explosion point is located, b represents the height of the underground cavern side wall where the explosion point is located, k, β1And β2Q is the explosive amount and R is the distance between the predicted point and the explosion point.
4. The system for predicting blasting vibration velocity of the central area of the underground cavern side wall according to claim 3, wherein the prediction model is obtained by performing parameter fitting on a preset model based on output signals of the plurality of vibration sensors and the first configuration parameter, and specifically comprises:
using the output signals of the plurality of vibration sensors as V, and performing parameter fitting on a prediction model by combining first configuration parameters to obtain k and β1And β2Thereby obtaining a prediction model.
5. The system for predicting blasting vibration velocity of the central area of the side wall of the underground cavern as claimed in claim 3, wherein the prediction model satisfies the following constraint relationship:
6. the system for predicting blasting vibration velocity of a central area of a side wall of a underground cavern as recited in claim 1, wherein the distribution positions of the plurality of vibration velocity sensors are located on the same straight line.
7. The system of claim 6, wherein the plurality of vibration rate sensors are equally spaced.
8. The system for predicting blasting vibration velocity of the central area of the side wall of the underground cavern as recited in claim 1, wherein the plurality of vibration velocity sensors and the processing module are connected in a wireless manner.
9. A method for predicting blasting vibration velocity of a side wall central area of an underground cavern, which is applied to a processing module in a system according to claim 1, and is characterized by comprising the following steps:
determining a mode;
receiving first configuration parameters in a training mode, wherein the first configuration parameters comprise coordinates of the vibration sensors in a first coordinate system, the length and the height of the side wall of the first underground cavern, the distance between the vibration sensors and a first explosion point and a first explosive amount;
responding to a starting signal, receiving output signals of the vibration speed sensors, and performing parameter fitting on a preset model based on the output signals of the vibration speed sensors and the first configuration parameter to obtain a prediction model;
receiving second configuration parameters in a prediction mode, wherein the second configuration parameters comprise the coordinates of a prediction point in a second coordinate system, the distance between the prediction point and a second explosion point, the second explosive quantity, and the length and the height of a second underground cavern side wall where the second explosion point is located;
and substituting the second configuration parameter into the prediction model to obtain the vibration speed of the predicted point.
10. The method for predicting blasting vibration velocity of the central area of the side wall of the underground cavern as claimed in claim 9, wherein the prediction model is as follows:
wherein V represents the vibration speed of the prediction point, (x, y) represents the coordinate of the prediction point, a represents the length of the underground cavern side wall where the explosion point is located, and b represents the height of the underground cavern side wall where the explosion point is locatedDegree, k, β1And β2Q is the explosive amount and R is the distance between the predicted point and the explosion point.
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