CN105627851A - New method for rock blasting deformation research - Google Patents

Abstract

The invention relates to a new method for rock blasting deformation research and belongs to the field of the technical research of the basic theory, the rock mechanics, the blasting theory and application of the basic theory, the rock mechanics and the blasting theory. The method comprises the following steps of acquiring the blasting action and blasting deformation through experiments or actual observation, calculating the strength of the blasting action, calculating the blasting deformation speeds in all directions, calculating the porosities and the solidities of the rock stratums in all directions, calculating the limit anti-blasting strengths of the stratums in all directions, and determining an economical, reasonable, safe and reliable blasting mode capable of meeting the production requirements, the explosive charging amount and other parameters. The new method has the beneficial effects that according to the relational theory and formula between blasting and deformation, a blasting mechanism and an experiment, observation and analysis calculation method for researching the blasting deformation basic laws are provided, so that scientization, systematization, theorization and practicality of blasting experiments, observation and analytical calculation are truly achieved, the blank that the blasting mechanism is undefined in the world for a long term is filled, and a giant leap in the blasting theory research history is realized.

Description

A kind of new method of rock blasting Study on Deformation

Technical field

The present invention relates to the new method of a kind of rock blasting Study on Deformation, it belongs to rationale, rock mechanics, theory of blasting and application technical research field thereof.

Background technology

Theory of blasting is exactly study the theory of relationship schedule between explosive charge percussion and explosion deformation-destruction. Inherently, controlled blasting deformation because of have two aspects: effect that explosive charge produces and by the character of explosion object (material with spatial group zoarium).

At present, existing theory of blasting nearly ten kinds in the world. Theory of blasting the earliest is the failure theory overcoming rock gravity and frictional force, in succession occurred in that the scope of freedom and minimum burden principle later, explosion Hydrodynamics Theory, maximum crushing stress, shear stress, tension strength theory, shock wave, stress wave activity are theoretical, echo stretching action is theoretical, it is theoretical that detonation gas expands thrust, the accurate quiet wedge pressure intreractive theory of detonation gas, stress wave is theoretical with detonation gas combined effect, energy intensity is theoretical, and function balance is theoretical, explosive funnel theory and the blasting fracgmentation theory of mechanics of livingston. It is theoretical that the theory of blasting that the present age generally acknowledges is mainly explosion wave, stress wave and detonation gas combined effect.

No matter it is early stage theory of blasting or contemporary theory of blasting, all there is a kind of common defects: explosive charge is not enough with by the quantitative relationship knowledge of regularity of explosion deformation of body, all of theory of blasting all can not find the theoretical formula describing blast action with explosion deformation.

The eighties in 20th century, create effect in China and learn. Effect is learned and is disclosed the organic growth a kind of naturally quantitative relationship generally observed that develops and unify rule, and this certain amount of unified rule gives the unified approach studying various problems. This method be further correct understanding explosion rule, set up more scientific theory of blasting and established good basis.

Summary of the invention

The present invention is directed to existing explosive charge and by the deficiency of the quantitative relationship knowledge of regularity of explosive body deformability, it is provided that the new method of a kind of rock blasting Study on Deformation.

The technical scheme is that

1, the effect relation between blast and rock deformation

The effect that blast produces has its particularity: quickly (momentary action), high intensity, act on around from all directions, working substance is rapidly converted into the impact energy of the photon group with flank speed motion by explosive and the gas expansion energy of high-speed motion, has high temperature, high pressure, action intensity is big, act on the features such as swift and violent. The particularity of this effect result in the particularity by working substance change. Under detonation, the rapid deformation failure of sudden and violent body, and generate the shock wave to surrounding transmission, often formed fluctuation change shape with explosion center for wave source by working substance at a distance. Therefore, the material equation of change described under detonation should be the relation equation between effect and fluctuation.

According to effect unity of opposites equation group $\left\{\begin{array}{c}{A}_F+A_T=A,\\ A_F=EA,\\ A_T=TA,\\ E+T=1.\end{array}\right.$ The action intensity �� impacting expansion any point in wavefront surface that blast produces produces two amounts: real action intensity and empty action intensity, is designated as �� respectively_TAnd ��_F, the relation between three is by equation group $\left\{\begin{array}{c}{\mathrm{\σ}}_F+{\mathrm{\σ}}_T=\mathrm{\σ}\\ {\mathrm{\σ}}_F=E\mathrm{\σ}\\ {\mathrm{\σ}}_T=T\mathrm{\σ}\\ E+T=1\end{array}\right.$ Determine. Wherein, solidity that T and E is known respectively as in wavefront surface any point and wasting time, it is respectively used to describe the immutable character of arbitrfary point and character can be changed. According to the �� in this equation group_F=E �� equation, it may be determined that in wavefront surface, the wave equation of any particle is

$y={\∫}_{\frac{x}{u}}^t\frac{E(\mathrm{\σ}+\mathrm{\ρ}gt)dt}{\mathrm{\ρ}}.$

In formula, �� represents the material density in wavefront surface; �� represents the detonation intensity that in wavefront surface, particle is subject to; X represents the distance between wave source and wavefront; U represents velocity of wave; T represents the wave time of shock wave; G represents acceleration of gravity; What E represented particle wastes time (variable pitch). The equation is referred to as the general equation that between detonation and blastic deformation, motion, unified relationship rule describes. Wherein,

$\mathrm{\σ}=\frac{A}{S}=\frac{Ft}{S},$

A represents Blast Shock amount, and F represents Blast Shock power, and t represents the Blast Shock time, is also the wave time of shock wave.

Relevant with explosive character and explosive charge size by action intensity �� value. �� value is it is generally required to determine by experiment, and its defining method can refer to following method:

The actuating quantity size that unit mass explosive charge can produce is determined by bore shooting. Unit mass explosive explodes in bore, promotes bullet to run, and the maximum momentum that bullet runs can be considered to be approximately equal to the promotion momentum that unit mass explosive charge produces, and is designated as I₀, its dimension is " meter per second ". Quality of explosive m and the I used in engineering explosion₀The long-pending Blast Shock amount that can produce equal to explosive, be designated as A, its dimension is " Kilogram-Meter Per Second ". That is,

A=mI₀.

First this actuating quantity acts on the wave source face of shock wave, is then passed to wavefront surface. Assume that any wavefront surface area is S, then, it is �� that wavefront surface accepts the percussion intensity of explosive charge generation,

$\mathrm{\σ}=\frac{A}{S}=\frac{{\mathrm{mI}}_0}{S}.$

Rock stratum particle, except accepting the effect of Blast Shock intensity ��, is also controlled by action of gravity, and the actuating quantity (action intensity) that particle is produced by gravity is ��_G=�� gt, so, the actuating quantity that rock stratum particle accepts in explosion deforms is equal to �� and ��_GThe vector sum of two amounts, i.e. the instant effect amount that rock stratum particle accepts is

${\mathrm{\σ}}_t=\mathrm{\σ}+{\mathrm{\σ}}_G=\frac{{\mathrm{mI}}_0}{S}+\mathrm{\ρ}gt.$

Other actuating quantity, as inhibition amount, rubbing action amount, overlying material produce suppressing action amount all without the concern for, this tittle is included among its nature and characteristic value. When research fluctuation, action of gravity can also be left out, because action of gravity at this moment belongs to restraining factors, it is possible to be comprised among environmental properties parameter. But must take into gravity when motion is dished out in research, because at this moment gravity constitutes the part of active role, is not belonging to restraining factors.

In explosion metaboly, and not all particle all runs with the vibration mode of wave surface, and some particle can be spilled in moment, do projectile motion. Such as the part mass being spilled over from explosive funnel, move along a curved path with projectile motion form. This motion can describe by equation below:

$l={\∫}_0^t\frac{E(\mathrm{\σ}+\mathrm{\ρ}gt)dt}{\mathrm{\ρ}}.$

Its curve movement is parabolically.

No matter it is infinite medium or half infinite medium, the actuating quantity that homogeneity equivalent explosive charge produces is equal to A, the action intensity that wavefront surface is produced is equal to ��, change with nature of ground difference Deng destructiveness (explosion deformation) situation in explosive charge explosion situation, because being the restraining factors of controlled blasting rock deformation by the character of explosion rock stratum. Loose, cranny development rock stratum its waste time greatly, antiknock ability is little, and rock stratum closely knit, complete solidity is big, and antiknock ability is big. With explosion center be core quick-fried internal, the region that crack pores'growth, voids content are big, content of material is little is wasted time greatly, it is easy to deformation failure; Closely knit complete area solidity is big, is unlikely to deform destruction. In short, in blasting phenomena, which direction is weak, and the deformation failure intensity in which direction is just big. Therefore, there is no need to distinguish infinite medium or half infinite medium according to effect theory research explosion rule.

2. the method for relationship schedule research between blast and deformation

Explosion deformation is divided into two kinds of situations to be studied by traditional theory: situation that situation is exploded in powder charge in infinite medium and powder charge is exploded in half infinite medium. The present invention does not differentiate between both situations, only according to the momentum relationship formula between explosion and damaged deformation, they is unified research.

Learning according to effect, the universal relation equation that powder charge is exploded between the effect produced and the fluctuation of rock particle or motion in rock stratum is

$y={\∫}_{\frac{x}{u}}^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}$ Or $l={\∫}_0^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}.$

If representing explosion deflection by the space increments produced by acting surface (wave source is by acting surface or wavefront surface) displacement, then, the universal relation equation between explosion deformation and its governing factor is

$V=\∫\∫\left({\∫}_{\frac{x}{u}}^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}\right)dS$ Or $V=\∫\∫\left({\∫}_0^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}\right)dS.$

In formula, �� �� dS represents and carries out area integral to by acting surface (wavefront surface) S. The equation have expressed the relationship schedule between blast action, the character of running environment, displacement increment (comprising elastic displacement and plastic displacement) and the change being subject to acting surface overall that in detonation space, any one is accepted by effect particle.

Powder charge is exploded in infinite medium, and the relation equation between deformation and the blast action of medium is exactly the relation equation between fluctuation and effect:

$y={\∫}_{\frac{x}{u}}^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}$ Or $V=\∫\∫\left({\∫}_{\frac{x}{u}}^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}}\right)dS.$

This deformation process is given qualitative description by traditional theory: " powder charge is explosion time in infinite medium; form the cavity (that is compressional zone; the most obvious in soil-structure interactions and soft rock) of expansion nearby except powder charge outward, also outwards sequentially forms crush zone, Fractured zone (also known as destruction region) and travelling-wave shock district (see Fig. 1) from charge center. In crush zone, rock is strongly pulverized and is produced bigger plastic deformation, forms a series of slide surface at 45 �� with radial direction. In Fractured zone, this body structure of rock does not change, but forms radial Radial crack, is sometimes also formed with the tangential crack of ring-type between Radial crack. Rock in travelling-wave shock district does not have any destruction, only shakes, and its intensity increases with the distance from explosion center and weakens gradually, so that being wholly absent. "

It is as follows that the present invention gives the Quantitative research method of anti-detonation intensity under quantitative study explosion deformation properties and blast action according to effect theory:

Metering blasting agential time, and measure the incremental deformation �� l of wavefront surface, further according to the least action I that quality of explosive m, unit quality of explosive produce₀, relational expression between wavefront surface area S

$\mathrm{\σ}=\frac{A}{S}=\frac{{\mathrm{mI}}_0}{S},$

Calculate wavefront surface and accept the action intensity of blast action, then, just can according to equation $y={\∫}_{\frac{x}{u}}^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}},$ By calculating the character index obtaining wavefront surface. That is, when certain detonation, wasting time of wavefront surface is

$E=\frac{\mathrm{\ρ}a}{\mathrm{\σ}};$

The solidity of wavefront surface is

$T=1-E=1-\frac{\mathrm{\ρ}a}{\mathrm{\σ}};$

The antidetonation strength of wavefront surface is

${\mathrm{\σ}}_{max}=T\mathrm{\σ}=(1-\frac{\mathrm{\ρ}a}{\mathrm{\σ}})\mathrm{\σ}=\mathrm{\σ}-\mathrm{\ρ}a.$

Powder charge is exploded in infinite medium, forms the cavity of expansion nearby in powder charge. Different medium, different in kind, different rock-layers different in kind, the cavity size formed in waiting explosive charge explosion is different. Accordingly, the generated nature parameters E value in space can be obtained according to relational expression E=�� a/ �� and character parametric T values and corresponding antidetonation strength �� can not be generated_max=T �� value (does not generate the maximum effect intensity level that cavity can be resisted).

The size reflection rock stratum resistance to crusing character of crush zone and crushability matter. Crushability matter is E=�� a/ ��, and resistance to crusing character is T=1-E, and the broken intensity of ultimate compressive is ��_max=T ��.

The size reflection rock stratum resistance to fracture character of Fractured zone (destruction region) and rupturable character. Rupturable character is E=�� a/ ��, and resistance to fracture character is T=1-E, and limit resistanee to rupture is ��_max=T ��.

Vibrations (wave zone) reflect vibrations (fluctuation) character of rock stratum. The method of research vibrations (fluctuation) property is too. Namely wavefront surface particle can vibratility be E=�� a/ ��, and wavefront surface particle can not vibratility be T=1-E, and the shock strength limit (keeping not shaking the maximum impact action intensity that can resist) of wavefront surface particle is ��_max=T ��.

People find in practice: " powder charge is exploded in half infinite medium; after charging explosion; except forming crush zone, Fractured zone and vibrations district in solid dielectric below powder charge (assuming that medium Free Surface and is level above powder charge); above powder charge, a part of rock will be broken; depart from former medium, forms explosive funnel. "

According to effect theory, the generation of explosive funnel is also the character being decided by effect and rock stratum, and its rule can describe with the unified rule equation of explosion deformation. Description method is as follows:

The actuating quantity that controlled blasting funnel generates is the part in blast action amount, as shown in Figure 2. By acting surface area, blow-up point rock is designated as S, and explosive funnel rock is designated as S by acting surface area_L, the quality being spilled over rock in explosive funnel is designated as m, then, in explosive funnel, rock by the service quality m blast action amount accepted in explosion is

A_L=S_L��;

As for whether m can be spilled over, how to deform, how to crush, also by many factors co-controllings such as nature of ground, degree of crushing, crack hole state, blast hole depth, big gun hole seal degrees. The equation of motion being spilled over rock stratum particle is

$l={\∫}_0^t\frac{E\mathrm{\σ}dt}{\mathrm{\ρ}},$

The operation equation being spilled over quality m is

$l={\∫}_0^t\frac{{\mathrm{ES}}_L\mathrm{\σ}dt}{m}.$

Relational expression between funnel volume and blast action that unit mass (1kg) explosive charge is formed is

$V=\frac{{\mathrm{ES}}_L\mathrm{\σ}}{\mathrm{\ρ}v}.$

In formula, V represents blasting crater volume; E represents degree of can dishing out; S_LRepresent the contact surface area between explosive funnel rock and explosive; �� represents rock density; V represents that rock is spilled over speed.

Relation between explosive buried depth (minimum burden is designated as W) and blast action, it is possible to derive according to the geometrical relationship between blasting crater volume and explosive buried depth, i.e. setSo,

Powder charge buried depth coefficient delta in traditional theory and blast action, nature of ground are just united by this. Namely

In formula, W_CRepresent powder charge buried depth marginal value. The buried depth coefficient delta of traditional theory introducing powder charge is primarily to the explosion reasonability problem of solution " shot depth is much properly, how much suitable explosive payload is ", it is taken at practical purpose completely, the relation between blast action and explosion deformation and rock property is not discussed. The partial content taken passages in traditional theory is presented herein below:

" the funnel volume V that explosion is formed_u(��=W/W relevant to the buried depth coefficient delta of powder charge_C). As ��=1 i.e. W=W_CTime, V_u=0; In this case, blast action is only limited to inside rock mass, it is impossible to arrive Free Surface. As �� < 1, form explosive funnel, its cone-apex angle and volume and reduce with �� and constantly increase. When �� value is reduced to certain value, V_uReach maximum, minimum burden W at this moment₀It is called optimum burden, ��₀=W₀/W_CIt is called optimum embedding coefficient. If continuing to reduce �� value, though funnel cone-apex angle can continue to increase (can not infinitely increase, can only increase to certain limit), V_uValue but reduces on the contrary. As the i.e. W=0 in ��=0, though still can form explosive funnel, but its volume is only small, and this powder charge being placed in rock surface is called exposed powder charge, is commonly called as dobie. When the cone-apex angle forming explosive funnel is less, in funnel, fragmented rock only swells, it does not have the throwing phenomenon of a large amount of rocks. The powder charge that this effect occurs is called loosening powder charge, and the explosive funnel of its formation is called broken funnel or loosening funnel. The explosion only forming loosening funnel is called standing. After the cone-apex angle of explosive funnel is more than certain limit, fragmented rock will be spilled over funnel. The powder charge that this effect occurs is called throwing powder charge, and the explosive funnel of its formation is called thrown-off funnel. Around thrown-off funnel, generally also remaining with part broken but fail the rock being spilled over, this part rock is called and loosens cone, and it belongs to the part remained in loosening funnel. After throwing process terminates, a part of rock falls back in thrown-off funnel. Additionally, a part of rock being deposited in around funnel also can be slipped in funnel. The explosive funnel can seen on the scope of freedom is called visible funnel, its degree of depth is called visible depth, it is designated as P. in crush zone, Fractured zone and funnel forming process, the intensity of shock wave (stress wave) weakens significantly, dielectric rupture can not have been made again beyond rupture zone, can only causing the vibration elastic of medium particle, namely the vibrations scope of particle is vibrations districts. The scope in vibrations district is very big. Within the scope of this, from the place close to charge center, shockproofness is big; From the place away from charge center, shockproofness is little. "

Learning according to effect, the generation of explosive funnel is the same with other deformation, all realizes under influencing factor and restraining factors co-controlling. Actually, the effect that explosion produces is from blow-up point radial active state towards periphery, in same wavefront surface, radiation effects intensity (action density) is each to approximately equal, but each by the material on action direction line and spatial distribution state and unequal. According to effect theory, the voids content on action direction line is big, content of material is little, and it is wasted time greatly, is easy for deformation failure; Otherwise, if content of material is big, voids content is little, its solidity is big, wastes time little, is just not easy deformation failure. The crack and the hole that exist in rock stratum are spatial compositional, Bao Kongshi spatial distribution district, it is space beyond minimum burden (scope of freedom), these spatial distribution directions are wasted time big, it is good that deformable destroys character, non-deformable destruction character is poor, so, it is easily deformed destruction in those directions. Between research all directions are acted on and deform, the equation of relationship schedule is all

$l={\&Integral;}_0^t\frac{E\mathrm{\&sigma;}dt}{\mathrm{\&rho;}}.$

Actuating quantity �� and its E value of wasting time that the move distance (including fluctuation distance and vibrations distance) of particle is subject to it are directly proportional: actuating quantity �� and mobility index E value that particle is subject to are big, and its range ability is just big. Why forming explosive funnel in engineering explosion, it it is critical only that wastes time greatly on explosive funnel direction.

Compared with prior art, the invention has the beneficial effects as follows: broken the not scientific ideology existed in conventional blast theory, the explosion that the effect that establishes is learned deforms new theory and new method. According to the relational theory between explosion and deformation and formula, The present invention gives blast mechanism, and give research explosion the deformation experiment of basic law, observation, analysis calculation method, make blasting experiment, observation and analytical calculation be truly realized scientific, systematization, theorize, practical, fill up the blank spot of long-term indefinite blast mechanism in the world, it is achieved that a huge leap forward on theory of blasting research history.

Accompanying drawing explanation

Fig. 1 is the powder charge deformation condition schematic diagram that explosion time produces in infinite medium;

Fig. 2 is that explosive funnel generates the schematic diagram of relation between blast action;

Fig. 3 is the actuating quantity test experiments schematic diagram that unit quality explosive charge produces.

Detailed description of the invention

Below in conjunction with accompanying drawing, principles of the invention and feature being described, example is served only for explaining the present invention, is not intended to limit the scope of the present invention.

The first step, is determined by experiment the maximum effect intensity that unit mass explosive can produce, and test method is as follows:

By packaging spherical in shape for unit mass medicated bag, being positioned in structure as shown in Figure 3, then ignition charge, observation is applied the operation time of the move distance of component, movement velocity and burst period and component, calculates action intensity. Clocking method: install autotimer, and image video recording and carry out timing mensuration. Computing formula:

$\mathrm{\&sigma;}=\frac{mv}{S}.$

Second step, the explosion deformation rule of test rock stratum, it is determined that wasting time and solidity (character) and antiknock ability of rock stratum, method of testing is as follows:

Blast hole drilling, charge explosion, location parameter, analytical calculation.

3rd step, solves actual production problem, as required as determined borehole depth, explosion dose etc.

In a word, new theory of blasting can sum up as follows with step to explosion research method out:

A, by experiment or obtain blast action amount and explosion deflection by actual observation;

B, calculating Blasting strength;

C, calculate each to explosion deformation velocity;

D, calculate each wasting time and solidity to rock stratum;

E, calculate each limit antidetonation strength to rock stratum;

F, determine economy, reasonable, safe and reliable, meet parameter values such as producing the blasting method method of needs and explosive payload.

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.

Claims (3)

1. the new method of a rock blasting Study on Deformation, it is characterised in that including:

(1) the effect relation between blast and rock deformation, comprises the steps,

A, according to effect unity of opposites equation group $\left\{\begin{array}{c}{A}_F+A_T=A\\ A_F=EA\\ A_T=TA\\ E+T=1\end{array}\right.$ Drawing, the action intensity �� impacting expansion any particle in wavefront surface that blast produces produces real action intensity and empty action intensity two amount, is designated as �� respectively_TAnd ��_F, it is determined that the relation equation group between three $\left\{\begin{array}{c}{\mathrm{\&sigma;}}_F+{\mathrm{\&sigma;}}_T=\mathrm{\&sigma;}\\ {\mathrm{\&sigma;}}_F=E\mathrm{\&sigma;}\\ {\mathrm{\&sigma;}}_T=T\mathrm{\&sigma;}\\ E+T=1\end{array}\right.;$

Wherein, T represents the solidity of any particle, i.e. immutable character in wavefront surface; E represents wasting time of any particle in wavefront surface, can be changed character;

B, according to ��_F=E ��, it may be determined that the wave equation of any particle in wavefront surface, the general equation that namely between detonation and blastic deformation, motion, unified relationship rule describes is

$y={\&Integral;}_{\frac{x}{u}}^t\frac{E(\mathrm{\&sigma;}+\mathrm{\&rho;}gt)dt}{\mathrm{\&rho;}};$

In formula, �� represents the material density in wavefront surface, and �� represents the detonation intensity that in wavefront surface, particle is subject to, and x represents the distance between wave source and wavefront, and u represents that velocity of wave, t represent the wave time of shock wave, and g represents that acceleration of gravity, E represent wasting time of particle;

(2) method of relationship schedule research between blast and deformation, learns according to effect,

A, powder charge explosion time in rock stratum, the universal relation rule equation between explosion deformation and its governing factor is $V=\&Integral;\&Integral;\left({\&Integral;}_{\frac{x}{u}}^t\frac{E\mathrm{\&sigma;}dt}{\mathrm{\&rho;}}\right)dS;$

In formula, �� �� dS represents by acting surface S, wavefront surface is carried out area integral;

B, powder charge explosion time in infinite medium, the universal relation rule equation between explosion deformation and its governing factor is $y={\&Integral;}_{\frac{x}{u}}^t\frac{E\mathrm{\&sigma;}dt}{\mathrm{\&rho;}}.$

2. the new method of a kind of rock blasting Study on Deformation according to claim 1, it is characterised in that in explosion metaboly, some particle can be spilled in moment, do projectile motion, its curve movement equation is $l={\&Integral;}_0^t\frac{E(\mathrm{\&sigma;}+\mathrm{\&rho;}gt)dt}{\mathrm{\&rho;}}.$

3. the new method of a kind of rock blasting Study on Deformation according to claim 2, it is characterised in that

A, powder charge explosion time in rock stratum, the universal relation rule equation between explosion deformation and its governing factor is $V=\&Integral;\&Integral;\left({\&Integral;}_0^t\frac{E\mathrm{\&sigma;}dt}{\mathrm{\&rho;}}\right)dS;$

B, powder charge explosion time in infinite medium, the universal relation rule equation between explosion deformation and its governing factor is $V=\&Integral;\&Integral;\left({\&Integral;}_{\frac{x}{u}}^t\frac{E\mathrm{\&sigma;}dt}{\mathrm{\&rho;}}\right)dS.$