CN113076653A - Dangerous rock mass blasting dynamic stability analysis method considering size effect - Google Patents
Dangerous rock mass blasting dynamic stability analysis method considering size effect Download PDFInfo
- Publication number
- CN113076653A CN113076653A CN202110409373.4A CN202110409373A CN113076653A CN 113076653 A CN113076653 A CN 113076653A CN 202110409373 A CN202110409373 A CN 202110409373A CN 113076653 A CN113076653 A CN 113076653A
- Authority
- CN
- China
- Prior art keywords
- blasting
- dangerous rock
- rock mass
- dangerous
- earthquake
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 239000011435 rock Substances 0.000 title claims abstract description 310
- 238000005422 blasting Methods 0.000 title claims abstract description 186
- 238000004458 analytical method Methods 0.000 title claims abstract description 33
- 230000005476 size effect Effects 0.000 title claims abstract description 15
- 238000000034 method Methods 0.000 claims abstract description 66
- 238000004364 calculation method Methods 0.000 claims abstract description 64
- 230000001133 acceleration Effects 0.000 claims abstract description 52
- TZCXTZWJZNENPQ-UHFFFAOYSA-L barium sulfate Chemical compound [Ba+2].[O-]S([O-])(=O)=O TZCXTZWJZNENPQ-UHFFFAOYSA-L 0.000 claims abstract description 32
- 230000014509 gene expression Effects 0.000 claims abstract description 20
- 230000008859 change Effects 0.000 claims abstract description 11
- 230000009471 action Effects 0.000 claims description 31
- 230000002238 attenuated effect Effects 0.000 claims description 6
- 238000012545 processing Methods 0.000 claims description 3
- 238000012546 transfer Methods 0.000 claims description 3
- 230000000694 effects Effects 0.000 abstract description 9
- 230000005484 gravity Effects 0.000 abstract description 8
- 238000010276 construction Methods 0.000 abstract description 7
- 238000011156 evaluation Methods 0.000 abstract description 6
- 230000002265 prevention Effects 0.000 abstract description 3
- 238000010586 diagram Methods 0.000 description 15
- 238000006243 chemical reaction Methods 0.000 description 9
- 230000006378 damage Effects 0.000 description 7
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 7
- 230000008569 process Effects 0.000 description 6
- 239000002360 explosive Substances 0.000 description 5
- 238000011160 research Methods 0.000 description 5
- 238000001228 spectrum Methods 0.000 description 5
- 238000005520 cutting process Methods 0.000 description 4
- 230000004044 response Effects 0.000 description 4
- 239000000463 material Substances 0.000 description 3
- 230000035515 penetration Effects 0.000 description 3
- 230000032683 aging Effects 0.000 description 2
- 238000005452 bending Methods 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000009191 jumping Effects 0.000 description 2
- 230000003068 static effect Effects 0.000 description 2
- 230000008093 supporting effect Effects 0.000 description 2
- 230000001550 time effect Effects 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004590 computer program Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000005474 detonation Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000002706 hydrostatic effect Effects 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 230000035772 mutation Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000011158 quantitative evaluation Methods 0.000 description 1
- 238000010008 shearing Methods 0.000 description 1
- 230000000087 stabilizing effect Effects 0.000 description 1
- 230000035882 stress Effects 0.000 description 1
- 239000002352 surface water Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/62—Analysis of geometric attributes of area, perimeter, diameter or volume
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Geophysics And Detection Of Objects (AREA)
Abstract
The invention discloses a method for analyzing blasting dynamic stability of a dangerous rock mass by considering size effect, which comprises the steps of establishing a geometrical model of the dangerous rock mass, carrying out striping on the dangerous rock mass on the basis of a striping method, and calculating the area, the quality and the gravity center position of each 'micro-strip block' on the basis of geometrical relation; the method comprises the steps of establishing a basic expression of the acceleration of the blasting earthquake according to given frequency and amplitude of the blasting earthquake, considering the change of an incident initial phase in the vertical direction and the horizontal direction, solving blasting earthquake loads on each micro-bar block by combining Newton's second law, accurately solving the blasting earthquake loads of the dangerous rock mass in the vertical direction and the horizontal direction under different initial phase conditions according to a load superposition effect, obtaining stability coefficients of the dangerous rock mass under different initial phase combination conditions in two directions, and providing certain reference and basis for analysis and evaluation of blasting dynamic stability of the dangerous rock mass, prevention and control of dangerous rock mass disasters in engineering construction and blasting control by taking the minimum stability coefficient value as a calculation result of the blasting dynamic stability of the dangerous rock mass.
Description
Technical Field
The invention relates to the technical field of dangerous rock mass stability analysis, in particular to a method for analyzing blasting dynamic stability of dangerous rock mass by considering size effect.
Background
China is a multi-mountain country, the area of mountains accounts for two thirds of the total land area of the country, and the mountains and high valleys in the western region are deep, the geological structure is complex, and the hidden danger of geological disasters is widely distributed. In mountain geological disasters, dangerous rock body collapse has the characteristics of high risk, concealed distribution, complex geological conditions, serious post-disaster fruit and the like. With the continuous expansion of human living development space to mountainous areas, dangerous rock mass collapse becomes one of the most common rock slope hazard sources, and especially when dangerous rock masses exist nearby in the construction process of infrastructure engineering and need to be cleaned or excavated by using blasting technology, if the blasting vibration effect is not properly controlled in the construction operation, the side slope dangerous rock masses can be induced to collapse, so that the life and property safety of engineering and surrounding people can be threatened.
With the enhancement of ergonomic activities, blasting techniques are widely used, but with a series of negative effects, blasting vibrations are one of them. If the blasting vibration is improperly controlled in the construction process, the safety of adjacent equipment and building structures can be affected, and the blasting damage area in a certain range is formed on dangerous rocks and side slopes, so that the bearing capacity and the stability of the rocks are reduced.
In order to control the influence of blasting vibration on dangerous rock masses, firstly, the stability of the dangerous rock masses under the action of blasting earthquake load is evaluated, but the evaluation is limited to the geological conditions, the shape and the size of the dangerous rock masses and the complexity of the action of blasting ground vibration force load. The method solves the problem that the dynamic load action condition of the blasting earthquake on the dangerous rock mass cannot be truly reflected in the conventional method, and has theoretical significance and practical value for preventing and controlling the geological disaster of the collapse of the dangerous rock mass in engineering construction.
The calculation of the stability of the dangerous rock mass is the key for preventing and treating the geological disaster of dangerous rock mass collapse, and the scientific and accurate calculation method of the stability of the dangerous rock mass has important practical significance for predicting the collapse of the dangerous rock mass.
The mechanical parameters of Liujiando and the like for calculating the stability of the dangerous rock mass are selected by adopting a neural network, and the instability mechanism of the rock mass slope is considered to be reasonable by using a pull-shear yield criterion to analyze stress and strain [ Liujiando, Shaoyangyu, Chengxiao, and the like.
CHEKKOV V N utilizes a three-dimensional nonlinear theory to comprehensively analyze the plasticity characteristics of a stratified rock mass, and provides a precise calculation method for the stability of a regular stratified semi-infinite medium [ CHEKKOV V N. elasticity for the plastic properties of rock in stability schemes for a structured rock mass [ J ]. International Applied Mechanics,2007,43(12): 1359-.
The dangerous rock is regarded as a rigid body by ChenhongKai and the like, a dangerous rock power calculation model is established based on a combination of a power time-course analysis method, the nature of the damage of the dangerous rock is the fracture damage of a main control structure surface by a fracture mechanics theory [ ChenhongKai, Xianhufu, Tanghongmei, and the like ], a dangerous rock stability analysis method [ J ]. an application mechanics report, 2009,26(2):278 Bu 282], [ ChenhongKai, Tanghongmei, Wang Rong ] three gorges reservoir area dangerous rock stability calculation method and an application [ J ]. rock mechanics and engineering report, 2004,23(4):614-619], [ ChenhongKai, Tanghongmei ] dangerous rock main control structure surface strength parameter calculation method [ J ]. engineering geology report, 2008,16(1):37-41], [ ChenhongKai, Zhongyuntai, Tanghongmei ] collapse and a sliding type dangerous rock collapse analysis-based power clearing blasting stability calculation method [ J ]. vibration and impact, 2014,33(15) 31-34, Daohoukai, Xianhufu, Tanghongmei, dangerous rock stability fracture mechanics calculation method J, Chongqing university school newspaper, 2009,32(4) 434-437.
Liuyuan and the like analyze the stability of the high and steep rocky slope under the action of earthquake by using an improved Newmark method, and a discrete integral fracture network method is provided [ Liuyuan, Wangxinghua.
On the basis of fully considering earthquake force, hydrostatic pressure and dangerous rock body characteristics, Liuwei Hua and the like research the stability of different types of dangerous rock bodies under different main control structure surface combinations, and provide a stability calculation method corresponding to dangerous rock bodies [ Liuwei Hua, Huang run autumn, dangerous rock stability quantitative evaluation research [ J ] roadbed engineering, 2014(6):51-57 ].
The Wanglinfeng and the like establish a calculation method for the aging stability of the dangerous rock mass after considering the time effect on the basis of the fracture mechanics theory, and consider that the fracture toughness of the structural surface at different positions of the dangerous rock mass is different; in addition, from the energy perspective, the horizontal thick layer falling type dangerous rock mass under the earthquake action is researched, the critical extension length of the main control structure surface of the dangerous rock mass is obtained, and a dangerous rock mass stability calculation method [ Wanglinfeng, Chenhongkai and Tanghongmei ] considering the soft rock supporting action is established, and a dangerous rock stability reliability aging calculation method [ J ] based on fracture mechanics and optimization theory is provided, which is reported by Wuhan university students, 2013 and 35(4):68-72], [ Wanglinfeng, Chenhongkai, Tanghongmei, etc.. earthquake action falling type dangerous rock stability analysis [ J ]. underground space and engineering report, 2013,9(5): 1191. 1196], [ Wanglinfeng, Chenhongkai, Tanghongmei ] Critical rock stability analysis considering soft rock mass support [ J ] Proc. report on railroad science and engineering, 2014,11(2): 65-70].
Deng jumping and the like provide a method for calculating the stability of dangerous rock masses under the action of dynamic load, reasonably illustrate that the calculation results of the stability of some slippage type dangerous rock masses are small, but collapse damage does not occur [ Deng jumping, Zhongyutao, fracture mechanics method for calculating the stability of dangerous rock masses under the action of power [ J ]. Changjiang river of people, 2015(13):33-38], [ Chentao, slump type dangerous rock tip point mutation model research [ J ]. Ningxia university school report (Nature science edition), 2015,36(4):346 and 350).
Li Jiahao et al adopts the principle of vibration Mechanics, establishes the relationship between the natural vibration frequency and cohesion of the dangerous Rock mass through experiments, and proposes that the natural vibration frequency of the dangerous Rock mass can be used as a reference index of the damage degree of the Rock mass [ Li Jia trench, Wu Gift boat, time effect analysis of the stability of the dangerous Rock mass [ J ]. Changjiang river, 2014,45(14):89-92], [ Li Hu, Wangjiliang, Yanjing, etc.. the high-steep Rock slope block stability research method and application [ J ]. hydroelectric energy science, 2011,29(12):85-87], [ Huangjiang, Chun, Jifeng, etc.. the application and discussion of three-dimensional laser scanning technology in the investigation of high-side slope Rock mass [ J ]. Yangtze academy of sciences, 2013,30(11):45-49], [ DU Y, XIE M W, JIANG Y J, et al. 2017,50(4):1-5].
Ding Wang, etc. establishes a calculation model of a main control structural surface containing a through section and a non-through section for a dangerous rock mass, and deduces a stability calculation formula [ Ding Wang, Zhou Yun Tao, dangerous rock stability calculation [ J ] based on a locking section model of the main control structural surface, Changjiang river of people, 2015,46(24):72-77 ].
A critical rock body is subjected to ultimate tensile strength of a rock body as a main criterion of stability by a measuring macro ring and the like, and a stability calculation model (measuring macro ring, Liujiankun, Zhang group, and the like) containing longitudinal cracks of the critical rock body is constructed.
In summary, the existing evaluation of the blasting vibration influence of the dangerous rock mass mainly refers to an analysis method of natural earthquake, the peak acceleration of blasting vibration is uniformly applied to the dangerous rock mass in a quasi-static manner, but the blasting earthquake is obviously different from the natural earthquake in the characteristics of frequency, wavelength and the like, and the influence of the size of the dangerous rock mass is added, so that the traditional method cannot truly reflect the dynamic load action condition of the blasting earthquake on the dangerous rock mass. The existing method and advantages and disadvantages:
(1) the quasi-static method is a method for calculating dynamic stability of a side slope by using the earliest and the broadest method. In the aspect of the influence of blasting vibration on the dangerous rock mass, limit balance analysis is basically carried out by using a pseudo-static method in a reference specification, and loads are applied in the direction with the worst stability of the dangerous rock mass according to the application method of natural earthquake. The method is characterized in that the instantaneous effect of seismic force is equivalent to the acceleration in the horizontal direction and the vertical direction and is applied to a rock mass structure, then calculation is carried out based on the extreme balance theory, and the safety coefficient of a potential sliding body is determined by solving a static balance equation or a moment balance equation of the potential unstable sliding body.
However, the blasting earthquake is significantly different from the natural earthquake in terms of frequency, wavelength, and the like; the quasi-static method does not consider the influence of geological conditions and shape and size of the dangerous rock mass, and the stability analysis result can be deviated; the load is applied according to the application method of natural earthquake, the load with uniform size is applied in the direction with the most unfavorable stability of dangerous rock mass, and the actual condition that the blasting earthquake acts on the dangerous rock mass cannot be reflected.
(2) The reaction spectrum method is to convert dynamic problem into static problem for calculation, and applies the principle that the total response of the structure is the superposition of the responses of all vibration modes. The reaction spectrum method comprises the steps of firstly constructing a reaction spectrum according to the recording of seismic wave time-courses, then calculating the maximum response of each order of vibration mode of the structure according to the reaction spectrum, and then calculating the total maximum response through a certain mode combination algorithm.
The theory is only a concept in an elastic range, and a reaction spectrum method cannot well reflect the possible inelastic characteristics of a plurality of structures in the actual seismic reaction; the whole maximum earthquake reaction of the structure when the structure enters the elastic-plastic state can be given out only in a general way, and the whole process of the earthquake reaction of the structure cannot be given out.
(3) The basic principle of the time-course analysis method is that the dynamic motion equation of the material is gradually iterated to carry out integral solution according to the elastic and inelastic characteristics of the material, and when the solution calculation is carried out, the frequency, amplitude and duration of an earthquake need to be considered, and the landform and geological structure conditions of a landslide body also need to be considered, so that the time-course method can be used for carrying out slope nonlinear analysis, the changes of displacement, speed, acceleration and the like of each point in the slope body at any moment are obtained, and the stability of the slope is analyzed according to the change influence.
The time-course analysis method accurately analyzes the deformation of the landslide from a microscopic angle, but from a macroscopic angle, the method is applied less in actual engineering, takes the nonlinear reaction of materials into consideration, needs to complete analysis by a computer program, and is not intuitive enough to calculate the stability of the landslide; the change of the load along with time is considered, but the change of the load along with the size effect of the dangerous rock mass is not considered; the calculation process is very complex and results require a lot of analysis and careful checking.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for analyzing stability of blasting dynamics of a dangerous rock mass in consideration of a size effect, which can provide certain references and bases for analysis and evaluation of stability of blasting dynamics of the dangerous rock mass, prevention and control of disasters of the dangerous rock mass in engineering construction, and blasting control. The technical scheme is as follows:
a method for analyzing blasting dynamic stability of a dangerous rock mass in consideration of size effect comprises the following steps:
step 1: simplifying and assuming the analysis object;
step 2: determining the two-dimensional shape type of the dangerous rock mass: assuming that coordinates of any three vertexes in four sides of a rectangle of the two-dimensional section image of the dangerous rock mass are unchanged, only changing one vertex coordinate to obtain 8 basic shapes of the quadrilateral dangerous rock mass;
and step 3: calculating the area of the two-dimensional section image of the dangerous rock mass: determining the geometric parameters of the dangerous rock mass, establishing a dangerous rock mass geometric model, striping the dangerous rock mass to obtain a plurality of micro-strip blocks, calculating the area of each micro-strip block based on the geometric relation, and finally summing to obtain the two-dimensional plane area of the dangerous rock mass;
and 4, step 4: calculating the blasting earthquake load: calculating blasting earthquake acceleration according to a propagation formula of blasting earthquake waves, calculating the mass of each micro-strip block of the dangerous rock body according to a mass calculation formula, calculating blasting earthquake loads acting on each micro-strip block in the horizontal radial direction and the vertical direction, summing to obtain the blasting earthquake loads acting on the whole dangerous rock body in the horizontal radial direction and the vertical direction, analyzing stability limit balance of the dangerous rock body under the action of the blasting earthquake, considering the change of different initial phases (0-2 pi) in the x and y directions, obtaining stability coefficients of the dangerous rock body under the combination condition of different initial phases in the two directions, and taking the minimum stability coefficient value as a blasting dynamic stability calculation result of the dangerous rock body.
Further, the simplification and assumption in step 1 include:
1) strip-to-strip of the dangerous rock mass without considering the strip-to-strip friction;
2) the blasting earthquake load acting on each micro-bar block is considered to be independent, and the moment action of each micro-bar block on the weight center of the dangerous rock is ignored;
3) the blasting seismic waves are not attenuated within the range of the dangerous rock mass;
4) the frequency components of the blasting seismic waves are simplified into sine wave processing, the frequency of the sine wave is consistent with the main frequency of the blasting seismic waves, the vertical and horizontal wavelengths of the blasting seismic waves along the dangerous rock mass are the same, and the acceleration amplitude and the acceleration frequency are consistent.
Further, the step 3 specifically includes:
step 31: establishing a coordinate system, inputting each coordinate point of the dangerous rock mass, and sequentially determining the positions of A (x1, y1), B (x2, y2), C (x3, y3) and D (x4, y4) in the anticlockwise direction; appointing a value of a bar score n, and carrying out bar scoring on the dangerous rock mass;
step 32: determining the area A of the ith micro-bar block according to the relative position relation of each coordinate pointiAnd the location of the center point;
step 33: calculating the area A of the whole two-dimensional dangerous rock massw：
Further, the step 4 specifically includes:
step 41: calculating blasting earthquake acceleration
Simplifying the blasting seismic wave into a sine wave, and according to a propagation formula of the blasting seismic wave:
X(t)＝A0 sin(2πft) (1)
and obtaining a blasting vibration velocity expression by differentiating t through the expression (1):
similarly, the t is derived according to the formula (2) to obtain an expression of the blasting vibration acceleration:
a(t)＝A04π2f2 sin(2πft+π) (3)
simplifying the expression of the blasting vibration acceleration as follows:
a(t)＝Asin(2πft+φ0) (4)
according to the relationship between the propagation distance x of the blasting seismic wave, the propagation velocity v of the wave and the time t:
x＝vt (5)
assuming that the blasting vibration acceleration on the dangerous rock mass is not attenuated, the amplitude, the frequency and the wave velocity of the blasting vibration acceleration in the horizontal radial direction and the vertical upward direction are all considered to be consistent, and the energy transfer of the blasting seismic wave is carried out in a single wave mode, the expression form of the blasting vibration acceleration in the horizontal radial direction and the vertical upward direction is obtained as follows:
in the formula: a. the0The amplitude of the blasting seismic wave is used; t is the propagation time; a (x), a (y) are horizontal radial and vertical upward blasting vibration acceleration expressions; a is the amplitude of the blasting vibration acceleration; f is the frequency of the blasting vibration acceleration; v is the propagation velocity of the blasting seismic wave; phi is ax、φyRepresenting the initial phases of blasting vibration acceleration in horizontal radial direction and vertical upward direction;
step 42: calculating the earthquake load of dangerous rock body blasting
According to a mass calculation formula, the mass of the ith micro-bar block of the given dangerous rock mass is obtained:
mi＝ρVi＝ρAi Bw (8)
where ρ is the density of the dangerous rock mass, ViVolume of the ith micro-bar; b iswThe height of the dangerous rock mass in the direction vertical to the section plane;
the blasting earthquake load F acted vertically upwards by the ith micro-bar blockyiComprises the following steps:
Fyi＝mxiaxi (9)
blasting earthquake load F acted in horizontal radial direction of ith micro-bar blockxiComprises the following steps:
Fxi＝myiayi (10)
in the formula, mxiThe quality of the ith micro-bar block of the dangerous rock mass in the horizontal direction is obtained; m isyiThe mass of the ith micro-bar block of the dangerous rock mass in the vertical direction; a isxi、ayiThe blasting vibration acceleration values in the horizontal radial direction and the vertical upward direction are acted on the corresponding ith micro-bar block;
vector superposition is carried out on the horizontal radial and vertical upward blasting earthquake loads acting on each micro-bar block, and the horizontal radial and vertical upward blasting earthquake loads F acting on the whole dangerous rock mass are obtainedxAnd Fy：
According to horizontal radial and vertical upward blasting earthquake loads Fx and Fy, the stability coefficients of the dangerous rock mass under different initial phase combination conditions in two directions are obtained by considering the change of different initial phases (0-2 pi) in the x and y directions, and then the minimum stability coefficient value is used as the blasting dynamic stability calculation result of the dangerous rock mass.
The invention has the beneficial effects that: on the basis of traditional ultimate balance analysis, the invention provides a method for analyzing blasting dynamic stability of dangerous rock mass by considering size effect, establishes a geometrical model of the dangerous rock mass, divides the dangerous rock mass on the basis of a division method, and calculates the area, the mass and the gravity center position of each micro-bar block on the basis of geometrical relation; according to the given blasting earthquake frequency and amplitude, a basic expression of the blasting earthquake acceleration is established, the change of the incident initial phase is considered in the vertical direction and the horizontal direction, the blasting earthquake load on each micro-bar block is worked out by combining the Newton's second law, the blasting earthquake loads of the vertical direction and the horizontal direction of the dangerous rock mass under different initial phase conditions are accurately worked out according to the load superposition effect, the minimum value is extracted as the calculation result of the stability of the dangerous rock mass, and certain reference and basis are provided for the analysis and evaluation of the blasting dynamic stability of the dangerous rock mass, the prevention and control of the dangerous rock mass disaster in engineering construction and the blasting control.
Drawings
FIG. 1 is a diagram of 8 basic shapes of quadrilateral dangerous rock masses.
Fig. 2 is a schematic diagram of cutting a dangerous rock mass.
FIG. 3 is a flowchart of a procedure for calculating the area of a dangerous rock mass
Fig. 4 is a diagram illustrating the blast vibration acceleration.
FIG. 5 is a schematic diagram of calculation of blasting seismic load
FIG. 6 is a Hys1 dangerous rock mass stability calculation result diagram.
FIG. 7 is a Hys2 dangerous rock mass stability calculation result diagram.
FIG. 8 is a Qds1 dangerous rock mass stability calculation result diagram.
FIG. 9 is a Qds2 dangerous rock mass stability calculation result diagram.
FIG. 10 is a Zls dangerous rock stability calculation result chart.
Fig. 11 is a schematic view of a first type of sliding type mechanical model of a dangerous rock mass.
Fig. 12 is a schematic diagram of a second type slip type dangerous rock mechanical model.
Fig. 13 is a schematic diagram of a first-class dumping type dangerous rock body mechanical model.
Fig. 14 is a schematic diagram of a second type dumping type dangerous rock mechanical model.
Fig. 15 is a schematic view of a falling type dangerous rock body mechanical model.
Fig. 16 is a comparison graph of the calculation results of the stability of the dangerous rock mass.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
1. Basic assumptions
The process of blasting seismic waves and the vibration caused by the waves is a very complex problem and is comprehensively influenced by various factors such as the position of a blasting source, the explosive loading, the detonation mode, the propagation medium, the site conditions and the like. In the analysis of the blasting dynamic stability of the dangerous rock mass, the size effect of the dangerous rock mass cannot be ignored, and the influence of the frequency and the phase of blasting seismic waves and the size of the dangerous rock mass on the actual application condition of the blasting seismic load must be considered. The method establishes a method for analyzing the blasting dynamic stability of the dangerous rock mass by considering the size effect on the basis of the traditional ultimate balance analysis, the rigid body and the plane structure of the dangerous rock mass are assumed to be maintained unchanged, and the method is close to the practical situation as far as possible when blasting earthquake load is applied and calculated, but for convenient analysis, the following simplification and assumption are made:
(1) strip-to-strip of the dangerous rock mass without considering the strip-to-strip friction;
(2) the blasting earthquake load acting on each micro-bar block is considered to be independent, and the moment action of each micro-bar block on the weight center of the dangerous rock is ignored;
(3) the blasting seismic waves are not attenuated within the range of the dangerous rock mass;
(4) the frequency components of the blasting seismic waves are complex, the blasting seismic waves are simplified into sine wave processing, the frequency of the sine wave is consistent with the main frequency of the blasting seismic waves, the vertical and horizontal blasting seismic wave wavelengths along the dangerous rock mass are the same, and the acceleration amplitude and the acceleration frequency are consistent.
2. Two-dimensional shape type of dangerous rock mass
According to relevant literature research, the shape of a two-dimensional section image of a dangerous rock mass is mostly quadrangular. By combining the relative position relationship of the four vertexes of the quadrilateral dangerous rock mass, firstly, assuming that coordinates of any three vertexes in the four sides of the rectangle are unchanged, only one vertex coordinate is changed, and 8 basic shapes of the quadrilateral dangerous rock mass can be obtained through analysis, as shown in fig. 1.
Continuously evolving according to the 8 basic shapes of the quadrilateral dangerous rock mass and the rule (any three vertex coordinates are unchanged, only one vertex coordinate is changed), and finally counting the possible two-dimensional shapes of the quadrilateral dangerous rock mass researched by the method in MATLAB
3. Calculating the area of the dangerous rock mass
Because only a few discrete data about dangerous rock mass can be obtained in practical engineering, especially when the boundary is an irregular curve, the area calculation is complicated. In order to find a convenient and efficient area solving method, a two-dimensional image area calculation method of a quadrilateral dangerous rock mass is established by using MATLAB software programming, and the program is realized as follows: by inputting the coordinate values of 4 vertexes of the quadrilateral dangerous rock mass and the strip fraction n (when the method and the program are used, the strip fraction n of the dangerous rock mass can refer to the suggested value of the table 1), the area of each 'micro-strip block' can be obtained according to the area calculation formula of a triangle, a parallelogram and a trapezoid, and the principle, the algorithm steps and the precision of the method are carefully analyzed. The area calculation program comprises the following steps:
(1) firstly, establishing a coordinate system in MATLAB, inputting each coordinate point of the dangerous rock mass, and determining the coordinates points as A (x) in turn in the anticlockwise direction1，y1)、B(x2，y2)、C(x3，y3)、D(x4，y4) The position of (a); the value of the bar score n is specified and the dangerous rock mass is bar-graded as shown in fig. 2.
TABLE 1 reference value of fraction n of dangerous rock mass
(2) And determining the area of each micro bar block i and the position of the central point according to the relative position relation of each coordinate point.
(3) Calculating the area of the whole two-dimensional dangerous rock mass
(4) And finally forming a calculation program through debugging and checking (for the dangerous rock mass shown in the figure 2, the area size of each 'micro-bar block' of the dangerous rock mass has a trend of increasing from left to right, stabilizing and reducing).
According to the analysis steps, the area calculation program flow of the quadrilateral dangerous rock mass two-dimensional image can be determined, and the specific process is shown in fig. 3.
4. Calculation of explosive seismic loads
(1) Blasting seismic acceleration representation
Simplifying the blasting seismic wave into a sine wave, and according to a propagation formula of the blasting seismic wave:
X(t)＝A0 sin(2πft) (1)
and obtaining a blasting vibration velocity expression by differentiating t according to the expression 1:
similarly, t is derived according to formula 2 to obtain an expression of the blasting vibration acceleration:
a(t)＝A04π2f2 sin(2πft+π) (3)
for the sake of calculation convenience, the expression of the blasting vibration acceleration is simplified as follows:
a(t)＝Asin(2πft+φ0) (4)
according to the relationship between the propagation distance x of the blasting seismic wave, the propagation velocity v of the wave and the time t:
x＝vt (5)
according to the basic assumption 1, the blasting vibration acceleration on the dangerous rock mass is not attenuated; secondly, for the convenience of calculation, the amplitude, the frequency and the wave velocity of the horizontal radial blasting vibration acceleration and the vertical upward blasting vibration acceleration are all regarded as consistent, and the energy transfer of the blasting seismic wave is carried out in a single-wave mode, so that the representation forms of the horizontal radial blasting vibration acceleration and the vertical upward blasting vibration acceleration can be obtained:
in the above derived formula: a. the0The amplitude (m) of the blasting seismic wave; t is the propagation time(s); a (x), a (y) are horizontal radial and vertical upward blasting vibration acceleration expressions; a is the amplitude (m/s) of the blasting vibration acceleration2) (ii) a f is the frequency (Hz) of the blasting vibration acceleration; v is the propagation velocity (m/s) of the explosive seismic wave; phi is ax、φyIndicating the initial phases of blast vibration acceleration in the horizontal radial direction and the vertical upward direction. Fig. 4 is a waveform diagram of a typical blast vibration acceleration expression, taking a horizontal radial direction as an example.
(2) Calculation of earthquake load of blasting of dangerous rock mass
In order to determine the load size and direction of each part on the dangerous rock mass, the shape and the geometric dimension of the dangerous rock mass are comprehensively considered on the basis of a striping method, firstly, the coordinates of four vertexes of the quadrangular dangerous rock mass are given, secondly, the dangerous rock mass is striped, and the area of the ith 'micro-stripe block' of the dangerous rock mass is assumed to be AiAccording to a mass calculation formula:
mi＝ρVi＝ρAi Bw (8)
the mass of the ith ' micro-bar block ' of the given dangerous rock mass can be obtained, and then the mass is calculated according to the Newton's second law:
F＝ma (9)
the horizontal radial and vertical upward blasting seismic loads of the ith 'micro-bar' can be obtained, and a calculation diagram is shown in FIG. 5 by taking the horizontal radial acting load as an example.
According to FIG. 5, the combination of the formulas (6), (8) and (9) can determine the explosive seismic load F acting vertically and upwards on the ith' micro-baryi：
Fyi＝mxiaxi (10)
Similarly, the blasting seismic load F acting in the horizontal radial direction of each micro-bar block can be obtained according to the formulas (7), (8) and (9)xi：
Fxi＝myiayi (11)
In formulae (10) and (11):
Fxiand FyiThe method is characterized in that the method is characterized by comprising the following steps of (1) horizontally, radially and vertically upwards blasting seismic load (kN) acting on the ith 'micro block' of the dangerous rock mass; m isxiDividing the mass (kg) of any micro-strip block for the dangerous rock mass in the horizontal direction; m isyiDividing the mass (kg) of any micro-strip block for the dangerous rock mass in the vertical direction; a isxi、ayiFor blast vibration acceleration values (m/s) acting on the corresponding "microblocks" both horizontally and vertically upwards2)。
According to the formulas (10) and (11), the horizontal radial and vertical upward blasting seismic loads acting on each micro block are subjected to vector superposition, and the horizontal radial and vertical upward blasting seismic loads F acting on the whole dangerous rock mass can be obtainedxAnd Fy(kN)：
In the two summation formulas of the formulas (12) and (13), n is the strip fraction (taking an integer) of the dangerous rock mass.
In summary, given the type and size of dangerous rock mass, the input stripFraction n, applying a blasting earthquake acceleration to the dangerous rock mass, and calculating the horizontal radial and vertical upward blasting earthquake loads F according to Newton's second lawx、FyConsidering the change of different initial phases (0-2 pi) in the x and y directions, participating in stability limit balance analysis of dangerous rock masses in different instability modes under the action of the blasting earthquake by using blasting earthquake loads under the condition of different initial phase combinations in the two directions, and extracting the minimum stability coefficient under the condition of different phase combinations as a calculation result of the blasting dynamic stability of the dangerous rock masses.
5. Effect verification
Verifying the program, selecting the determined size of the dangerous rock mass (20 m grades are selected for verification in the embodiment), and taking the amplitude A of the blasting earthquake acceleration as 0.4m/s2The frequency f is 50Hz, the wave speed v is 4000m/s, and the bar fraction n is 50.
(1) Dangerous rock mass stability calculation analysis
The parameter values of the dangerous rock masses in different instability modes are shown in the table 2, and the calculation results are shown in the figures 6-7 and the table 3.
Table 220 m level dangerous rock parameter value
Note: h in the above table is the vertical depth (m) of the trailing edge crack; c is the cohesive force (kPa) of the main control structural surface of the dangerous rock mass;
the internal friction angle (degree) of the main control structure surface of the dangerous rock mass; sigmatIs the tensile strength (kPa) of the dangerous rock mass; k is a calculation coefficient of the bending moment of the dangerous rock mass, and the value is between 1/12 and 1/6 according to the section form.
TABLE 3 Critical rock stability calculation
The calculation result shows that the dynamic stability analysis method and program of the dangerous rock mass under the action of the blasting earthquake, which are provided by the method, consider the influence of factors such as the size of the dangerous rock mass, the frequency of the blasting earthquake and the like, and the calculated stability coefficient shows a certain periodic regular change along with the change of the initial phase of the incident of the blasting earthquake.
(2) Compared with the traditional pseudo-static method
The calculation formula of the stability of the dangerous rock mass under the action of the blasting earthquake is as follows:
sliding dangerous rock mass
The sliding dangerous rock mass mainly develops in a slope outside the slope, the steep dip cutting crack of the rear edge of the sliding dangerous rock mass is consistent with the slope inclination direction of the slope, the strength of the structural surface is further reduced under the action of rainwater, and the cutting crack of the rear edge can be further expanded and communicated to form a bedding main control structural surface. If under the external force action such as blasting earthquake load, when the gliding force of the rock mass is larger than the anti-sliding force on the main control structure surface, the slippage instability can occur, and basically the shearing failure is generated. The sliding dangerous rock mass under the action of the blasting earthquake load is divided into 2 categories according to the existence of the inclined and steep cracks on the trailing edge.
1) Sliding dangerous rock mass of the first kind
The first type of sliding dangerous rock mass has no steep dip crack at the trailing edge. AB represents a dangerous rock mass main control structure surface, and the length unit (m) theta of the dangerous rock mass main control structure surface is the included angle (DEG) between a sliding surface and a horizontal plane. The mechanical model is shown in fig. 11.
According to the dangerous rock mechanical model established in fig. 11, the dynamic stability coefficient Fs of the first type of slip dangerous rock under the action of the blasting earthquake load can be obtained as follows:
2) sliding dangerous rock mass of the second kind
The second type of sliding dangerous rock mass has a steep crack at the rear edge. The mechanical model is shown in fig. 12.
The dynamic stability coefficient F of the second sliding dangerous rock mass under the action of the blasting earthquake load can be obtained according to the dangerous rock mass mechanical model established in the figure 12sComprises the following steps:
in formulae (14) and (15):
theta is a slope angle (°) of the dangerous rock mass; h is the vertical height (m) of the dangerous rock mass; h is the vertical depth (m) of the trailing edge crack; g is the weight (kN) of the dangerous rock mass; fyBlasting seismic load (kN) acting in the vertical direction of the dangerous rock mass; fxBlasting seismic load (kN) acting in the horizontal direction of the dangerous rock mass; p is horizontal seismic force (kN/m)2)。
S is fracture water pressure (kN); u is the sliding surface water pressure (kN); c is the cohesive force (kPa) of the main control structural surface of the dangerous rock mass;
the internal friction angle (degree) of the main control structure surface of the dangerous rock mass; h iswThe water filling height (m) of the trailing edge crack is determined according to the crack depth and the catchment condition, and 1/3 is taken as the natural state to vertically penetrate through the crack height (m), namely hwH/3, 2/3 vertical penetration crack height (m) during a heavy rain condition, i.e., hw＝2h/3。
② dumping dangerous rock mass
The dumping dangerous rock mass mainly develops in a slope with a steep slope, the inclination degree of a rear main control structural plane of the dumping dangerous rock mass is approximately the same as that of a side slope, in addition, the rock mass at the lower part of the dangerous rock mass has a local air-facing phenomenon, and the gravity center of the dumping dangerous rock mass is positioned outside the supporting point of the base under most conditions. Under the effect of external forces such as blasting earthquake load, the main characteristics of formula of empting dangerous rock mass unstability destruction are: the steep main control structural plane at the rear edge of the rock mass is loosened, the strength is reduced, the cutting crack gradually expands, and the shattered rock mass has good near-empty conditions. The stability of the device is mainly influenced by the overturning moment, and when the overturning moment is larger than the anti-overturning moment under the action of the blasting earthquake load, the dangerous rock body is toppled and damaged. The dynamic stability analysis of the dumping type dangerous rock mass under the action of the blasting earthquake load is divided into 2 cases according to the condition that the gravity center of the dumping type dangerous rock mass is positioned on the inner side and the outer side of a dumping point O.
1) First class dumping dangerous rock mass
For the first type of dumping dangerous rock mass, the center of gravity is located inside the overturning point O. The mechanical model diagram is shown in fig. 13.
When the anti-tipping moment of the first type of tipping dangerous rock mass is greater than the tipping moment, the dangerous rock mass is kept in a stable state, and the stability coefficient F of the dangerous rock mass under the action of the blasting earthquake loadsComprises the following steps:
2) second type dumping dangerous rock mass
For the second type of dumping dangerous rock mass, the gravity center of the second type of dumping dangerous rock mass is positioned outside the dumping point O. The mechanical model is shown in fig. 14.
The stability coefficient of the dumping dangerous rock mass is generally lower than that of the first type, and the stability coefficient F of the second type of dumping dangerous rock mass under the action of blasting earthquake load is obtained according to the dumping moment and the anti-dumping moment at the dumping point OsComprises the following steps:
in formulae (16) and (17):
σtrepresenting a standard value (kPa) of tensile strength between the dangerous rock mass and the base; [ sigma ]t]Is the allowable value (kPa) of the tensile strength of the dangerous rock body; when the base is hard rock, [ sigma ] is takent]＝σt(ii) a And when the base is soft rock, taking the tensile strength standard value of the soft rock. a represents the horizontal distance (m) between the gravity center position of the dangerous rock mass and the overturning point; b represents the distance (m) between the bottom end of the main control structural plane of the dangerous rock body and the overturning point O.
h0Representing the vertical distance (m) from the center of gravity of the dangerous rock mass to the base. Theta is a slope angle (°) of the dangerous rock mass; h is the vertical height (m) of the dangerous rock mass; h is the vertical depth (m) of the trailing edge crack; g is the weight (kN) of the dangerous rock mass; fyBlasting seismic load (kN) acting in the vertical direction of the dangerous rock mass; fxIn the horizontal direction of the dangerous rock massAn upward acting explosive seismic load (kN); p is horizontal seismic force (kN/m)2) (ii) a S is fracture water pressure (kN);
hwthe water filling height (m) of the trailing edge crack is determined according to the crack depth and the catchment condition, and 1/3 is taken as the natural state to vertically penetrate through the crack height (m), namely hwH/3, 2/3 vertical penetration crack height (m) during a heavy rain condition, i.e., hw＝2h/3。
Falling type dangerous rock mass
The falling dangerous rock mass often appears on the slope of multiunit structural plane, and the inclination of its trailing edge main control structural plane is great, and is nearly perpendicular, and the bottom rock mass has mostly taken place the collapse of unstability and has destroyed, causes the bottom of falling dangerous rock mass to form and faces empty face. Under the effect of external forces such as blasting earthquake load, there is the crack near the structural plane of mother rock behind the formula of falling dangerous rock mass unstability destruction, if the effort that is used in main control structural plane position is greater than the tensile strength of rock mass, the crack can expand in the short time and develop, if dangerous rock mass can produce whole downwards quick fall after the rock bridge between the structural plane is pulled apart. The schematic diagram of the mechanical model of the falling type dangerous rock mass under the action of the blasting earthquake load is shown in fig. 15.
According to the falling dangerous rock mechanical model established in the graph 15, the dynamic stability coefficient F of the falling dangerous rock under the action of the blasting earthquake load is obtainedsComprises the following steps:
in formula (18):
theta is a slope angle (°) of the dangerous rock mass; sigmatIs the tensile strength (kPa) of the dangerous rock mass; h is the vertical height (m) of the dangerous rock mass; h is the trailing edge flaw vertical depth (m). k is a calculation coefficient of the bending moment of the dangerous rock mass, a value is taken between 1/12 and 1/6 according to the section form, and 1/6 is taken when the section is rectangular.
BwIs the average width (m) of the trailing edge primary control structure face; a is0The horizontal distance between the vertical load action point of the dangerous rock mass and the midpoint of the main control structure surface(m)；b0The vertical distance (m) between the horizontal load action point of the dangerous rock mass and the midpoint of the main control structure surface; g is the weight (kN) of the dangerous rock mass; fyBlasting seismic load (kN) acting in the vertical direction of the dangerous rock mass; fxBlasting seismic load (kN) acting in the horizontal direction of the dangerous rock mass; p is horizontal seismic force (kN/m)2) (ii) a S is fracture water pressure (kN).
hwThe water filling height (m) of the trailing edge crack is determined according to the crack depth and the catchment condition, and 1/3 is taken as the natural state to vertically penetrate through the crack height (m), namely hwH/3, 2/3 vertical penetration crack height (m) during a heavy rain condition, i.e., hw＝2h/3。
Under the condition that the calculation parameters are not changed, stability calculation is carried out on different instability mode dangerous rocks in the table 2 under the working conditions of load combination six (dead weight of dangerous rocks, fracture water pressure (rainstorm working condition) + blasting earthquake load) by using a traditional pseudo-static method, and the results are shown in tables 4 to 5.
TABLE 4 sliding type conventional pseudo-static method calculation results
TABLE 5 calculation results of the pour-type conventional pseudo-static method
TABLE 6 calculation results of falling-type conventional pseudo-static method
The results of the calculations in tables 4-6 are compared to the results of the present method, as shown in FIG. 16.
As can be seen from fig. 16, for a given dangerous rock mass example, under the condition of a certain parameter, the stability coefficient of the dangerous rock mass calculated by using the method and the program (wytwdxxs) is closer to the calculation result of the conventional pseudo-static method, but is greater than the calculation result of the conventional pseudo-static method, and the relative difference is between 5.1% and 8.2%, because the conventional pseudo-static method ignores the influence caused by the size effect of the dangerous rock mass, the peak load method is still applied in the worst direction according to the existing method, the calculated stability coefficient is smaller than the actual condition, and is more conservative in the aspect of safety evaluation; the method accurately reflects the actual application condition of the blasting earthquake load, and the calculation method and the program are reasonable and effective. And the calculation result relative difference of the two methods can be deduced to increase along with the increase of the size of the dangerous rock mass and the increase of the blasting earthquake frequency.
Claims (4)
1. A method for analyzing blasting dynamic stability of a dangerous rock mass in consideration of size effect is characterized by comprising the following steps:
step 1: simplifying and assuming the analysis object;
step 2: determining the two-dimensional shape type of the dangerous rock mass: assuming that coordinates of any three vertexes in four sides of a rectangle of the two-dimensional section image of the dangerous rock mass are unchanged, only changing one vertex coordinate to obtain 8 basic shapes of the quadrilateral dangerous rock mass;
and step 3: calculating the area of the two-dimensional section image of the dangerous rock mass: determining the geometric parameters of the dangerous rock mass, establishing a dangerous rock mass geometric model, striping the dangerous rock mass to obtain a plurality of micro-strip blocks, calculating the area of each micro-strip block based on the geometric relation, and finally summing to obtain the two-dimensional plane area of the dangerous rock mass;
and 4, step 4: calculating the blasting earthquake load: calculating the blasting earthquake acceleration according to a propagation formula of blasting earthquake waves, calculating the mass of each micro-strip block of the dangerous rock body according to a mass calculation formula, calculating the blasting earthquake load acting on each micro-strip block in the horizontal radial direction and the vertical direction, summing to obtain the blasting earthquake load acting on the whole dangerous rock body in the horizontal radial direction and the vertical direction, analyzing the stability limit balance of the dangerous rock body under the action of the blasting earthquake, obtaining the stability coefficients of the dangerous rock body under different initial phase combination conditions in two directions, and taking the minimum stability coefficient value as a program calculation result.
2. The method for analyzing blasting dynamic stability of dangerous rock mass considering size effect according to claim 1, wherein the simplification and assumption in step 1 comprises:
1) strip-to-strip of the dangerous rock mass without considering the strip-to-strip friction;
2) the blasting earthquake load acting on each micro-bar block is considered to be independent, and the moment action of each micro-bar block on the weight center of the dangerous rock is ignored;
3) the blasting seismic waves are not attenuated within the range of the dangerous rock mass;
4) the frequency components of the blasting seismic waves are simplified into sine wave processing, the frequency of the sine wave is consistent with the main frequency of the blasting seismic waves, the vertical and horizontal wavelengths of the blasting seismic waves along the dangerous rock mass are the same, and the acceleration amplitude and the acceleration frequency are consistent.
3. The method for analyzing blasting dynamic stability of dangerous rock mass considering size effect according to claim 1, wherein the step 3 specifically comprises:
step 31: establishing a coordinate system, inputting each coordinate point of the dangerous rock mass, and sequentially determining the positions of A (x1, y1), B (x2, y2), C (x3, y3) and D (x4, y4) in the anticlockwise direction; appointing a value of a bar score n, and carrying out bar scoring on the dangerous rock mass;
step 32: determining the area A of the ith micro-bar block according to the relative position relation of each coordinate pointiAnd the location of the center point;
step 33: calculating the area A of the whole two-dimensional dangerous rock massw：
4. The method for analyzing blasting dynamic stability of dangerous rock mass considering size effect according to claim 1, wherein the step 4 specifically comprises:
step 41: calculating blasting earthquake acceleration
Simplifying the blasting seismic wave into a sine wave, and according to a propagation formula of the blasting seismic wave:
X(t)＝A0 sin(2πft) (1)
and obtaining a blasting vibration velocity expression by differentiating t through the expression (1):
similarly, the t is derived according to the formula (2) to obtain an expression of the blasting vibration acceleration:
a(t)＝A04π2f2sin(2πft+π) (3)
simplifying the expression of the blasting vibration acceleration as follows:
a(t)＝Asin(2πft+φ0) (4)
according to the relationship between the propagation distance x of the blasting seismic wave, the propagation velocity v of the wave and the time t:
x＝vt (5)
assuming that the blasting vibration acceleration on the dangerous rock mass is not attenuated, the amplitude, the frequency and the wave velocity of the blasting vibration acceleration in the horizontal radial direction and the vertical upward direction are all considered to be consistent, and the energy transfer of the blasting seismic wave is carried out in a single wave mode, the expression form of the blasting vibration acceleration in the horizontal radial direction and the vertical upward direction is obtained as follows:
in the formula: a. the0The amplitude of the blasting seismic wave is used; t is the propagation time; a (x), a (y) are horizontal radial and vertical upward blasting vibration acceleration expressions; a is the amplitude of the blasting vibration acceleration; f is the blasting vibrationThe frequency of the acceleration; v is the propagation velocity of the blasting seismic wave; phi is ax、φyRepresenting the initial phases of blasting vibration acceleration in horizontal radial direction and vertical upward direction;
step 42: calculating the earthquake load of dangerous rock body blasting
According to a mass calculation formula, the mass of the ith micro-bar block of the given dangerous rock mass is obtained:
mi＝ρVi＝ρAiBw (8)
where ρ is the density of the dangerous rock mass, ViVolume of the ith micro-bar; b iswThe height of the dangerous rock mass in the direction vertical to the section plane;
the blasting earthquake load F acted vertically upwards by the ith micro-bar blockyiComprises the following steps:
Fyi＝mxiaxi (9)
blasting earthquake load F acted in horizontal radial direction of ith micro-bar blockxiComprises the following steps:
Fxi＝myiayi (10)
in the formula, mxiThe quality of the ith micro-bar block of the dangerous rock mass in the horizontal direction is obtained; m isyiThe mass of the ith micro-bar block of the dangerous rock mass in the vertical direction; a isxi、ayiThe blasting vibration acceleration values in the horizontal radial direction and the vertical upward direction are acted on the corresponding ith micro-bar block;
vector superposition is carried out on the horizontal radial and vertical upward blasting earthquake loads acting on each micro-bar block, and the horizontal radial and vertical upward blasting earthquake loads F acting on the whole dangerous rock mass are obtainedxAnd Fy：
According to the blasting earthquake loads Fx and Fy in the horizontal radial direction and the vertical upward direction, the change of different initial phases in the x direction and the y direction is considered, the blasting earthquake loads under the condition of different initial phase combinations in the two directions participate in the stability limit balance analysis of dangerous rocks in different instability modes under the action of blasting earthquake, and the minimum stability coefficient value under the condition of different phase combinations is extracted to serve as the blasting dynamic stability calculation result of the dangerous rocks.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110409373.4A CN113076653B (en) | 2021-04-16 | 2021-04-16 | Dangerous rock blasting dynamic stability analysis method considering size effect |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110409373.4A CN113076653B (en) | 2021-04-16 | 2021-04-16 | Dangerous rock blasting dynamic stability analysis method considering size effect |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113076653A true CN113076653A (en) | 2021-07-06 |
| CN113076653B CN113076653B (en) | 2022-10-11 |
Family
ID=76617730
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110409373.4A Active CN113076653B (en) | 2021-04-16 | 2021-04-16 | Dangerous rock blasting dynamic stability analysis method considering size effect |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113076653B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114330144A (en) * | 2022-02-15 | 2022-04-12 | 西南交通大学 | Slope dangerous stone early warning method, device, equipment and readable storage medium |
| CN115659586A (en) * | 2022-09-15 | 2023-01-31 | 四川大学 | Earthquake slope permanent displacement calculation method based on random concave-convex slope surface |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150185349A1 (en) * | 2013-12-30 | 2015-07-02 | Pgs Geophysical As | Methods and systems for optimizing generation of seismic images |
| CN107067333A (en) * | 2017-01-16 | 2017-08-18 | 长沙矿山研究院有限责任公司 | A kind of high altitudes and cold stability of the high and steep slope monitoring method |
| CN107330146A (en) * | 2017-05-26 | 2017-11-07 | 昆明理工大学 | It is a kind of while considering the jointed rock slope analysis of Ultimate upper bound method of translation and turning effect |
| CN108304637A (en) * | 2018-01-25 | 2018-07-20 | 武汉大学 | The recognition methods of Instability of Rock Slope pattern |
| CN109543326A (en) * | 2018-11-30 | 2019-03-29 | 浙江大学 | Open mine side slope rock mass discontinuity normal stress is classified the method for determination |
| CN110132714A (en) * | 2018-02-08 | 2019-08-16 | 山东高速济莱城际公路有限公司 | A kind of device and test method for testing irregular rock mass sample deformation parameter |
| US20200089823A1 (en) * | 2018-03-26 | 2020-03-19 | OrePro Holdings LLC | 3d block modelling of a resource boundary in a post-blast muckpile to optimize destination delineation |
-
2021
- 2021-04-16 CN CN202110409373.4A patent/CN113076653B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150185349A1 (en) * | 2013-12-30 | 2015-07-02 | Pgs Geophysical As | Methods and systems for optimizing generation of seismic images |
| CN107067333A (en) * | 2017-01-16 | 2017-08-18 | 长沙矿山研究院有限责任公司 | A kind of high altitudes and cold stability of the high and steep slope monitoring method |
| CN107330146A (en) * | 2017-05-26 | 2017-11-07 | 昆明理工大学 | It is a kind of while considering the jointed rock slope analysis of Ultimate upper bound method of translation and turning effect |
| CN108304637A (en) * | 2018-01-25 | 2018-07-20 | 武汉大学 | The recognition methods of Instability of Rock Slope pattern |
| CN110132714A (en) * | 2018-02-08 | 2019-08-16 | 山东高速济莱城际公路有限公司 | A kind of device and test method for testing irregular rock mass sample deformation parameter |
| US20200089823A1 (en) * | 2018-03-26 | 2020-03-19 | OrePro Holdings LLC | 3d block modelling of a resource boundary in a post-blast muckpile to optimize destination delineation |
| CN109543326A (en) * | 2018-11-30 | 2019-03-29 | 浙江大学 | Open mine side slope rock mass discontinuity normal stress is classified the method for determination |
Non-Patent Citations (5)
| Title |
|---|
| J XIE 等: "Deformation Failure Mechanism and Motion Laws of Near-horizontal Thick-layer with Thin-layer Columnar Dangerous Rock Mass in the Chishui Red Bed Area", 《IOP CONFERENCE SERIES：EARTH AND ENVIRONMENTAL SCIENCE》 * |
| LONGJUN DONG 等: "Some developments and new insights for environmental sustainbility and disaster control of tailings dam", 《JOURNAL OF CLEANER PRODUCTION》 * |
| 李程 等: "滑移式危岩体***振动动力稳定性研究", 《***器材》 * |
| 祝文化等: "特大型危岩体治理***开挖振动效应控制研究", 《***》 * |
| 许红涛等: "基于时程分析的岩质高边坡开挖***动力稳定性计算方法", 《岩石力学与工程学报》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114330144A (en) * | 2022-02-15 | 2022-04-12 | 西南交通大学 | Slope dangerous stone early warning method, device, equipment and readable storage medium |
| CN115659586A (en) * | 2022-09-15 | 2023-01-31 | 四川大学 | Earthquake slope permanent displacement calculation method based on random concave-convex slope surface |
| CN115659586B (en) * | 2022-09-15 | 2023-08-15 | 四川大学 | Seismic slope permanent displacement calculation method based on random concave-convex slope surface |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113076653B (en) | 2022-10-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Gong et al. | Numerical modelling of the effects of joint spacing on rock fragmentation by TBM cutters | |
| Ning et al. | Process analysis of toppling failure on anti-dip rock slopes under seismic load in southwest China | |
| CN113076653B (en) | Dangerous rock blasting dynamic stability analysis method considering size effect | |
| Liu et al. | Dynamic response and failure mode of slopes with horizontal soft and hard interbeddings under frequent microseisms | |
| Deng et al. | Model test and numerical simulation on the dynamic stability of the bedding rock slope under frequent microseisms | |
| Zhou et al. | Dynamic failure mode and dynamic response of high slope using shaking table test | |
| Huang et al. | Seismic response of loess-mudstone slope with bedding fault zone | |
| Jahromi et al. | The plurality effect of topographical irregularities on site seismic response | |
| Wang et al. | Particle mechanics modeling of the effect of aggregate shape on creep of durable rockfills | |
| Feng et al. | Excavation unloading‐induced fracturing of hard rock containing different shapes of central holes affected by unloading rates and in situ stresses | |
| CN111950160A (en) | Tunnel fracture slippage type rock burst determination method | |
| CN113435087B (en) | Method for analyzing local stability of cave surrounding rock | |
| Hu et al. | FDEM numerical study of the influence law of geostress on state and pressure of tunnel surrounding rock | |
| Xu et al. | Pseudo-dynamic analysis of a 3D tunnel face in inclined weak strata | |
| Lin et al. | Earthquake analysis of arch and gravity dams including the effects of foundation inhomogeneity | |
| CN117610448A (en) | Simulation method for predicting water burst quantity of mining fault | |
| Zhang et al. | Dynamic p-y curves for vertical and batter pile groups in liquefied sand | |
| Lu et al. | Numerical and experimental analyses for bearing capacity of rigid strip footing subjected to eccentric load | |
| Tai et al. | Effect of excitation frequency and joint density on the dynamic amplification effect of slope surface on jointed rock slopes | |
| Ali et al. | Response of circular footing on dry dense sand to impact load with different embedment depths | |
| Ling et al. | Effects of kinematic and inertial interaction on seismic responses of pile-structure system in liquefiable and non-liquefiable deposits | |
| Kouzer et al. | Ultimate bearing capacity of equally spaced multiple strip footings on cohesionless soils without surcharge | |
| Asaadi et al. | Numerical simulation of piles subjected to lateral spreading and comparison with shaking table results | |
| Wang et al. | Quantification of the active lateral earth pressure changes on retaining walls at the leading edge of steep slopes | |
| Taleb et al. | Assessment of slope stability with study parametric of faults (shear joints) using the lower and upper limit analysis method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |