CN105627851B - A kind of new method of rock blasting Study on Deformation - Google Patents
A kind of new method of rock blasting Study on Deformation Download PDFInfo
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- 238000005422 blasting Methods 0.000 title claims abstract description 84
- 239000011435 rock Substances 0.000 title claims abstract description 53
- 238000000034 method Methods 0.000 title claims abstract description 25
- 230000009471 action Effects 0.000 claims abstract description 79
- 239000002360 explosive Substances 0.000 claims abstract description 48
- 238000004880 explosion Methods 0.000 claims abstract description 40
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F42—AMMUNITION; BLASTING
- F42D—BLASTING
- F42D3/00—Particular applications of blasting techniques
- F42D3/04—Particular applications of blasting techniques for rock blasting
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Abstract
The present invention relates to a kind of new method of rock blasting Study on Deformation, and it belongs to basic theory, rock mechanics, theory of blasting and its application technical research field.It comprises the following steps：Blast action amount and explosion deflection are obtained by experiment or by actual observation；Calculate Blasting strength；Calculate each to explosion deformation velocity；Calculate it is each to rock stratum waste time and solidity；Calculate each limit antidetonation strength to rock stratum；It is determined that the parameter value such as blasting method method that is economic, reasonable, safe and reliable, meeting production needs and explosive payload.The beneficial effects of the invention are as follows：According to the relational theory and formula between explosion and deformation, give blast mechanism and study the experiment, observation, analysis calculation method of explosion deformation basic law, blasting experiment, observation is set to be truly realized scientific, systematization with analysis calculating, theorize, practical, the blank of long-term indefinite blast mechanism in the world has been filled up, has realized a huge leap forward on theory of blasting research history.
Description
Technical Field
The invention relates to a new method for rock blasting deformation research, and belongs to the field of basic theory, rock mechanics, blasting theory and application technology research thereof.
Background
The blasting theory is the theory for researching the relation rule between the explosive blast impact effect and blasting deformation-damage. Essentially, the factor controlling the deformation of the blast has two aspects: the effect of the explosive explosion and the nature of the object (material and space combination) to be blasted.
At present, nearly ten kinds of blasting theories exist in the world. The earliest blasting theory is a failure theory for overcoming the gravity and the friction force of a rock, and then a free surface and minimum resistance line principle, a blasting hydromechanics theory, a maximum pressure stress, shear stress and tensile stress intensity theory, a shock wave and stress wave action theory, a reflected wave stretching action theory, an explosive gas expansion thrust action theory, an explosive gas quasi-static wedge pressure action theory, a stress wave and explosive gas combined action theory, an energy intensity theory, a function balance theory, a Rivenston blasting funnel theory and a blasting fracture mechanics theory are sequentially presented. The blasting theory recognized by the modern times is mainly the theory of the combined action of the blast shock wave, the stress wave and the explosive gas.
Whether it is the early blasting theory or the current blasting theory, there is a common defect: the law of quantitative relation between explosive explosion and deformation of an object to be blasted is not well known, and a theoretical formula for describing blasting effect and blasting deformation cannot be found in all blasting theories.
In the 20 th century and the 80 th era, the theory of action was developed in China. The action discloses a natural quantitative relation unified rule which is generally observed by natural development and evolution, and the quantitative relation unified rule provides a unified method for researching various problems. The method lays a good foundation for further correctly knowing the blasting rule and establishing a more scientific blasting theory.
Disclosure of Invention
The invention provides a novel method for researching the blasting deformation of rock, aiming at the defect of the knowledge of the quantitative relation rule of the explosion of the existing explosive and the deformation of an exploded object.
The technical scheme for solving the technical problems is as follows:
1. the functional relationship between explosion and rock deformation
The effect of explosion generation has its particularity: the explosive has the characteristics of high speed (instant action), high strength, action on all sides around, quick conversion of action substances from the explosive into impact energy of photon groups moving at extremely high speed and gas expansion energy moving at high speed, high temperature, high pressure, high action strength, quick action and the like. This specificity of action leads to a specificity of change of the substance affected. Under the action of explosion, the explosive body is rapidly deformed and damaged, shock waves transmitted to the periphery are generated, and the remote affected substances often form a wave change form by taking an explosion center as a wave source. Therefore, the equation describing the change of matter under the effect of an explosion should be a relational equation between the effect and the fluctuation.
Unifying equation set according to action oppositionThe intensity σ of the impact expansion from an explosion at any point on the wave front yields two quantities: fruit of Chinese wolfberryAction intensity and deficiency action intensity, respectively denoted as σTAnd σFThe relationship between the three is represented by the equation systemAnd (4) determining. Where T and E are referred to as the real and imaginary, respectively, of any point on the wavefront, and are used to describe the non-changeable and changeable properties, respectively, of any point. According to σ in this system of equationsFThe wave equation for any particle on the wavefront can be determined as E σ equation
Where ρ represents the density of the substance on the wavefront surface; sigma represents the explosion action intensity of the particles on the wave front; x represents the distance between the wave source and the wavefront; u represents the wave velocity; t represents the fluctuation time of the shock wave; g represents the gravitational acceleration; e represents the degree of virtues (variability) of the particles. The equation is called as a general equation described by a unified relation rule between the explosion action and the explosion deformation and movement. Wherein,
a represents the action amount of the explosive shock, F represents the acting force of the explosive shock, t represents the acting time of the explosive shock, and is the fluctuation time of the shock wave.
The value of the applied strength sigma is related to the property of the explosive and the size of the explosive. The σ value generally needs to be determined by experiment, and the determination method can be referred to as the following method:
the action quantity which can be generated by unit mass explosive explosion is determined by shooting the gun chamber. The unit mass explosive explodes in the gun chamber to push the bullet to move, and the maximum momentum of the bullet in motion can be considered to be approximately equal to the pushing momentum generated by the unit mass explosive explosion and is marked as I0The dimension is "m/s". In engineeringMasses m and I of explosive used in blasting0The product of the two is equal to the amount of explosive impact action which can be generated by the explosive, is marked as A, and the dimension of the product is 'kilogram meter per second'. That is to say that the first and second electrodes,
A＝mI0.
the action acts first on the wave source surface of the shock wave and then is transferred to the wave front surface. Assuming that the area of the front surface of any wave is S, the intensity of the impact action generated by the explosion of the explosive on the front surface of the wave is sigma,
the formation mass point is controlled by the action of gravity, in addition to the action of the intensity of the explosive shock action σ, and the action amount (action intensity) of gravity on the mass point is σGRho gt, the formation particles therefore receive an amount of action equal to σ and σ in the blast deformationGThe vector sum of the two quantities, i.e. the quantity of real-time action received by the formation mass point is
Other acting amounts such as a retarding acting amount, a rubbing acting amount, and a pressing acting amount by an overlying substance are not necessarily considered, and these amounts are included in the characteristic values of the properties thereof. In the case of fluctuations, the effect of gravity may not be considered, since the effect of gravity is a limiting factor and may be included in the environmental property parameters. However, gravity must be taken into account when studying the throwing motion, since this time gravity constitutes an actively acting part and is not a limiting factor.
In the explosive deformation phenomenon, not all particles operate in the form of wave front vibration, and a part of particles are thrown out instantaneously to make parabolic motion. The part of the mass that is thrown out of the blast funnel, for example, is moved in a curved manner in the form of a projectile movement. This motion can be described by the following equation:
the motion curve is parabolic.
The action quantity generated by the explosion of the homogeneous equivalent explosive is equal to A no matter in an infinite medium or a semi-infinite medium, the action strength generated on the wave front is equal to sigma, and the destructive (explosion deformation) condition under the condition of equal explosive quantity explosion changes along with different rock stratum properties because the properties of the blasted rock stratum are the restriction factors for controlling the deformation of the blasted rock stratum. The loose and fractured developing rock stratum has large deficiency, small antiknock capability, dense and complete rock stratum with large compactness and great antiknock capability. In an explosion body taking an explosion center as a core, the fracture pore development, large space content and small substance content have large area virtues, and are easy to deform and damage; the compact and complete area has high solidity and is not easy to deform and destroy. In the blasting phenomenon, the strength of deformation and destruction in any direction is large in any direction, if any. Therefore, it is not necessary to distinguish between infinite media and semi-infinite media to study the blasting law according to the theory of action.
2. Method for researching relation rule between explosion and deformation
The traditional theory divides the blast deformation into two cases to study: a charge explosive in infinite medium and a charge explosive in semi-infinite medium. The invention does not distinguish the two situations, and only researches the two situations uniformly according to a momentum relation formula between blasting and destructive deformation.
According to the theory of action, the general relation equation between the action generated by the explosive charge exploding in the rock formation and the rock mass point fluctuation or movement is
Or
If the amount of deformation of the blast is expressed by the spatial increment produced by the displacement of the affected surface (wave source affected surface or wave front), the general equation of the relationship between the deformation of the blast and the control factors is
Or
Where ^ integral ^ dS represents the area integral of the affected surface (wavefront) S. The equation expresses the law of the relationship between the blasting action received by any affected particle in the blasting action space, the property of the operating environment, the displacement increment (including elastic displacement and plastic displacement) and the change of the affected surface as a whole.
The charge explodes in an infinite medium, and the relation equation between the deformation of the medium and the explosion action is the relation equation between the fluctuation and the action:
or
Conventional theory gives a qualitative description of this deformation process: "when a charge is exploded in an infinite medium, in addition to an enlarged cavity (i.e. a compression zone, most pronounced in earth media and soft rock) near the charge, a crush zone, a fracture zone (also known as a failure zone), and a wave vibration zone are formed in sequence from the center of the charge outwards (see fig. 1). In the crushing zone, the rock is strongly crushed and undergoes large plastic deformations, forming a series of slip planes at 45 ° to the radial direction. In the fracture zone, the rock structure is not changed, but radial fractures are formed, and annular tangential fractures are formed between the radial fractures. The rock in the wave vibration zone is not damaged at all, only vibrates, and the strength of the rock gradually weakens along with the distance from the center of the explosion so as to completely disappear. "
The invention provides a quantitative research method for quantitatively researching the blasting deformation property and the anti-blasting effect strength under the blasting effect according to the theory of action, which comprises the following steps:
measuring the blasting action time, measuring the deformation increment △ l of the wave front, and generating the maximum action I according to the mass m of the explosive and the mass of the unit explosive0Relation between wavefront surface area S
Calculating the action strength of the wave front subjected to blasting action, and then calculating the action strength according to an equationAnd calculating to obtain the property index of the wave front. That is, under certain explosive conditions, the virtual degree of the wavefront is
The wave front has the solidity of
The blast strength of the wave front is
The charge is detonated in an infinite medium to form an enlarged cavity in the vicinity of the charge. The different media are different from each other in that,the properties are different, the properties of different rock stratums are different, and the sizes of cavities formed in blasting with equal explosive quantity are different. Accordingly, the generable property parameter E value and the non-generable property parameter T value in the space and the corresponding antiknock intensity σ can be obtained from the relational expression E ═ ρ a/σmaxT σ value (maximum action intensity value against which no cavity is generated).
The size of the crush zone reflects the crush resistance and crushability properties of the formation. Crushability is E ═ rho/sigma, crush resistance is T ═ 1-E, and ultimate crush strength is sigmamax＝Tσ.
The size of the fracture zone (failure zone) reflects the fracture resistance and the fracturable nature of the formation. The breakable property is E ═ rho/sigma, the fracture resistance is T ═ 1-E, and the ultimate fracture resistance is sigmamax＝Tσ.
The vibrations (wave zone) reflect the vibrational (wave) nature of the formation. The same is true of the method of studying the vibration (fluctuation) property. That is, the vibratability of the wavefront particles is E ═ ρ a/σ, the non-vibratability of the wavefront particles is T ═ 1-E, and the limit of the seismic strength of the wavefront particles (the maximum impact strength that can be resisted by maintaining non-vibration) is σmax＝Tσ.
In practice it has been found that: "the charge is exploded in a semi-infinite medium, and after the charge is exploded, a part of the rock above the charge will be broken away from the original medium to form a blast funnel, except for the formation of a crushing zone, a fracture zone and a vibration zone within the solid medium below the charge (assuming that the free surface of the medium is above the charge and horizontal). "
According to the theory of action, the generation of the blasting funnel is also determined by the action and the nature of the rock stratum, and the law can be described by a blasting deformation unified law equation. The description method is as follows:
the amount of action generated by the control blast funnel is a fraction of the blast action amount, as shown in fig. 2. Recording the area of the rock acting surface of the blasting point as S and the area of the rock acting surface of the blasting funnel as SLRecording the mass of the rock thrown in the blasting funnel as m, then blastingThe mass m of rock in the hopper is subjected to a blasting action in an amount of
AL＝SLσ；
Whether m can be thrown out, how m is deformed and how m is crushed is controlled by various factors such as rock stratum properties, crushing degree, fracture pore state, blast hole depth, blast hole sealing degree and the like. The equation of motion of the thrown formation particle is
The operating equation of the thrown mass m is
The relation between the volume of a funnel formed by the explosion of a unit mass (1kg) of explosive and the explosion effect is
Wherein, V represents the volume of the blasting funnel; e represents the throwable degree; sLShowing the contact surface area between the blasting funnel rock and the explosive; ρ represents the rock density; v represents the rock throw velocity.
The relationship between the depth of penetration (minimum line of resistance, denoted as W) of the explosive and the blasting effect can be derived from the geometric relationship between the volume of the blasting funnel and the depth of penetration of the explosive, i.e. letThen it is determined that,
this unifies the depth coefficient of charge embedment, delta, with blasting and formation properties in conventional theory. Namely, it is
In the formula, WCRepresenting the critical value of the depth of charge. The traditional theory introduces the embedding depth coefficient delta of charging mainly aims at solving the blasting rationality problem of proper charging depth and proper charging amount, completely achieves the practical purpose, and does not discuss the relationship between blasting effect, blasting deformation and rock property. The following is a part of the abstract in the conventional theory:
"blast-formed funnel volume VuDependent on the depth of embedment factor delta (W/W)C). When Δ ═ 1, i.e. W ═ WCWhen, Vu0; in this case, the blasting action is confined to the interior of the rock mass and does not reach the free surface. When Δ < 1, a blast funnel is formed, the cone apex angle and volume of which increase continuously with decreasing Δ. When the value of delta decreases to a certain value, VuTo a maximum, at which the line of least resistance W is reached0Called line of optimum resistance, Δ0＝W0/WCReferred to as the optimal embedding coefficient. If the delta value is continuously reduced, the cone vertex angle of the funnel can be continuously increased (cannot be infinitely increased, and can only be increased to a certain limit), and VuThe value is instead decreased. When Δ is 0, i.e. W is 0, the blasting funnel can still be formed, but the volume is small, and the charge placed on the surface of the rock is called a naked charge and is commonly called a burnt cannon. When the cone apex angle forming the blasting funnel is smaller, the broken rock in the funnel only rises, and the throwing phenomenon of a large amount of rock is avoided. The charge that takes place is called loose charge and the blast funnel formed is called crushing funnel or loose funnel. A blast that forms only a loose funnel is called a loose blast. When the cone apex angle of the blasting funnel is larger than a certain limit, the broken rock will be thrown out of the funnel. The charge which effects this action is called a throw charge, and the resulting blast funnel is called a "throw chargeIs a throwing funnel. Around the throwing funnel there is usually also retained a part of the crushed but not thrown rock, called the loosening cone, which belongs to the part retained in the loosening funnel. After the throwing process is complete, a portion of the rock falls back into the throwing funnel. In addition, a portion of the rock that accumulates around the hopper may also slide down into the hopper. The blast funnel, visible on the free surface, is called the visible funnel, and its depth is called the visible depth, and is marked as p. The range of the vibration region is large. In the range, the vibration intensity is high at the position close to the charge center; the vibration intensity is small at the place far away from the center of the charge. "
According to the theory of action, the generation of the blasting funnel is realized under the control of both action factors and restriction factors, as well as other variants. In practice, the action produced by blasting is a state of action in radiation from the point of blasting to the periphery, and on the same wavefront, the intensity of radiation action (action density) is approximately equal, but the material and the spatial distribution state on each line of action direction are not equal. According to the theory of action, the space content on the action direction line is large, the material content is small, and the deformation and the damage are easy to occur if the degree of deficiency is large; on the contrary, if the material content is large and the space content is small, the material is large in the real degree and small in the virtual degree, and the material is not easy to deform and damage. The fractures and pores existing in the rock stratum are spatial components, the blast holes are spatial distribution areas, and the space is arranged outside the minimum resistance line (free surface), so that the virtual degree is large in the spatial distribution directions, the deformable destructive property is good, the non-deformable destructive property is poor, and the deformation destruction is easy in the directions. The equations for researching the relation rule between the acting and the deformation in each direction are
The distance of motion of a particle (including the fluctuation distance and the vibration distance) is proportional to the amount of action σ it is subjected to and the value of its imaginary degree E: the particles are subjected to large values of action sigma and mobility index E, and the travel distance is large. The key to forming the blast funnel in engineering blasting is the large degree of virtues in the direction of the blast funnel.
Compared with the prior art, the invention has the beneficial effects that: breaks through the unscientific concept existing in the traditional blasting theory and establishes a new blasting deformation theory and a new method of the action science. According to the relation theory and formula between blasting and deformation, the invention provides the blasting mechanism and provides the experiment, observation, analysis and calculation method for researching the basic law of blasting deformation, so that the blasting experiment, observation and analysis and calculation really achieve scientization, systematization, theorization and practicability, the blank point of long-term indefinite blasting mechanism in the world is filled, and a huge leap in the history of blasting theory research is realized.
Drawings
FIG. 1 is a schematic view of the deformation of a charge upon detonation in an infinite medium;
FIG. 2 is a schematic diagram of the relationship between blast funnel generation and blasting action;
FIG. 3 is a diagram of the experiment of the action amount test generated by unit mass explosive explosion.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
Firstly, determining the maximum action strength which can be generated by unit mass of explosive through experiments, wherein the test method comprises the following steps:
the unit mass explosive packages are packaged in a spherical shape and placed in a structure body as shown in figure 3, then the explosive is detonated, the movement distance, the movement speed and the explosion time of the acted component and the running time of the component are observed, and the action strength is calculated. The timing method comprises the following steps: an automatic timer is installed, and timing measurement is carried out by shooting and recording. Calculating the formula:
secondly, testing the blasting deformation rule of the rock stratum, and determining the deficiency, the real degree (property) and the anti-blasting capability of the rock stratum, wherein the testing method comprises the following steps:
and (4) blasting holes, charging and blasting, measuring parameters, and analyzing and calculating.
And thirdly, solving the actual production problem according to the requirement, such as determining the depth of a blast hole, the blasting explosive quantity and the like.
In summary, the blasting research method and steps given by the new blasting theory can be summarized as follows:
a. obtaining the blasting action amount and the blasting deformation amount through experiments or actual observation;
b. calculating the blasting effect strength;
c. calculating the deformation speed of each direction of blasting;
d. calculating the virtues and the realities of each rock stratum;
e. calculating the ultimate explosion strength of each rock stratum;
f. determining parameters such as an economical, reasonable, safe and reliable blasting mode method and loading capacity meeting production requirements.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (3)
1. A new method for researching rock blasting deformation is characterized by comprising the following steps:
(1) the functional relationship between the explosion and the deformation of the rock, comprising the steps of,
A. unifying equation set according to action opposition<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>F</mi> </msub> <mo>+</mo> <msub> <mi>A</mi> <mi>T</mi> </msub> <mo>=</mo> <mi>A</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>F</mi> </msub> <mo>=</mo> <mi>E</mi> <mi>A</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>T</mi> </msub> <mo>=</mo> <mi>T</mi> <mi>A</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>E</mi> <mo>+</mo> <mi>T</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>It is found that the action strength sigma of any particle on the wave front caused by impact expansion generated by explosion generates two quantities of real action strength and virtual action strength, which are respectively recorded as sigmaTAnd σFDetermining the relation equation set among the three<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&sigma;</mi> <mi>F</mi> </msub> <mo>+</mo> <msub> <mi>&sigma;</mi> <mi>T</mi> </msub> <mo>=</mo> <mi>&sigma;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&sigma;</mi> <mi>F</mi> </msub> <mo>=</mo> <mi>E</mi> <mi>&sigma;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&sigma;</mi> <mi>T</mi> </msub> <mo>=</mo> <mi>T</mi> <mi>&sigma;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>E</mi> <mo>+</mo> <mi>T</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein T represents the solidity of any particle on the wave front, i.e. the unchangeable property; e represents the degree of virtues of any mass point on the wave front, and the property can be changed;
B. according to σFThe wave equation of any mass point on the wave front can be determined as E sigma, namely the general equation described by the unified relation rule between the explosion action and the explosion deformation and motion is
<mrow> <mi>y</mi> <mo>=</mo> <mrow> <msubsup> <mo>&Integral;</mo> <mfrac> <mi>x</mi> <mi>u</mi> </mfrac> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>&sigma;</mi> <mo>+</mo> <mi>&rho;</mi> <mi>g</mi> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> </mrow> <mo>;</mo> </mrow>
In the formula, rho represents the density of a substance on a wave front surface, sigma represents the explosion action intensity of a mass point on the wave front surface, x represents the distance between a wave source and the wave front, u represents the wave speed, t represents the fluctuation time of shock waves, g represents the gravity acceleration, and E represents the virtual degree of the mass point;
(2) the method for researching the relation rule between explosion and deformation is characterized in that according to the action,
A. when the explosive charges explode in the rock stratum, the general relation rule equation between the explosion deformation and the control factors is as follows<mrow> <mi>V</mi> <mo>=</mo> <mo>&Integral;</mo> <mo>&Integral;</mo> <mrow> <mo>(</mo> <msubsup> <mo>&Integral;</mo> <mfrac> <mi>x</mi> <mi>u</mi> </mfrac> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mi>&sigma;</mi> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>S</mi> <mo>;</mo> </mrow>
Wherein;
B. when the explosive charges explode in an infinite medium, the general relation rule equation between the explosion deformation and the control factors is as follows<mrow> <mi>y</mi> <mo>=</mo> <mrow> <msubsup> <mo>&Integral;</mo> <mfrac> <mi>x</mi> <mi>u</mi> </mfrac> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mi>&sigma;</mi> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> </mrow> <mo>.</mo> </mrow>
2. The method as claimed in claim 1, wherein a part of particles are instantaneously thrown out and parabolic in the blasting deformation phenomenon, and the motion curve equation is<mrow> <mi>l</mi> <mo>=</mo> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mrow> <mo>(</mo> <mi>&sigma;</mi> <mo>+</mo> <mi>&rho;</mi> <mi>g</mi> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> </mrow> <mo>.</mo> </mrow>
3. The new method for rock blasting deformation research according to claim 2,
A. when the explosive charges explode in the rock stratum, the general relation rule equation between the explosion deformation and the control factors is as follows<mrow> <mi>V</mi> <mo>=</mo> <mo>&Integral;</mo> <mo>&Integral;</mo> <mrow> <mo>(</mo> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mi>&sigma;</mi> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>S</mi> <mo>;</mo> </mrow>
B. When the explosive charges explode in an infinite medium, the general relation rule equation between the explosion deformation and the control factors is as follows<mrow> <mi>V</mi> <mo>=</mo> <mo>&Integral;</mo> <mo>&Integral;</mo> <mrow> <mo>(</mo> <msubsup> <mo>&Integral;</mo> <mfrac> <mi>x</mi> <mi>u</mi> </mfrac> <mi>t</mi> </msubsup> <mfrac> <mrow> <mi>E</mi> <mi>&sigma;</mi> <mi>d</mi> <mi>t</mi> </mrow> <mi>&rho;</mi> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>S</mi> <mo>.</mo> </mrow>
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