CN117831655B - Surrounding rock blasting damage fracture range prediction method, storage medium and equipment - Google Patents
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Abstract
The invention discloses a surrounding rock blasting damage crack range prediction method which comprises the steps of obtaining working condition parameters, constructing a surrounding rock blasting damage crack range prediction model, then obtaining a surrounding rock damage partition crack range relational expression, and obtaining a surrounding rock blasting damage crack range based on the working condition parameters and the surrounding rock damage partition crack range relational expression. According to the method, the main stress, the initial ground stress, the initial damage, the borehole cavity expansion, the rock mass plastic damage and the shear expansion characteristics in the surrounding rock are comprehensively considered, so that the influence mechanism of the initial ground stress and the intermediate main stress on the crack range of the surrounding rock blasting damage can be revealed, the surrounding rock blasting efficiency is improved, and the crack range in the deep-buried tunnel drilling and blasting engineering practice is effectively predicted. The invention also discloses a storage medium and a device, wherein the storage medium and the device store a computer program, and the computer program can run the surrounding rock blasting damage fracture range prediction method.
Description
Technical Field
The invention relates to the technical field of deep-buried tunnel drilling and blasting, in particular to a prediction method, a storage medium and equipment for surrounding rock blasting damage crack range.
Background
The drilling and blasting construction technology still takes the dominant role in rock breaking and tunnel excavation due to the economical and efficient characteristics. Along with the continuous increase of the excavation depth, the remarkable characteristic of high ground stress exists in deep drilling and blasting engineering, so that phenomena such as overexcavation, underexcavation, additional damage and the like of surrounding rock are caused frequently, and the construction efficiency is reduced. Therefore, considering the effect of ground stress in blasting the surrounding rock is critical to control the fracture extent.
For prediction of the range of surrounding rock blasting damage fracture, existing studies include:
1. KANCHIBOTLA model, see "KANCHIBOTLA Seshadri-sarma,VALERY Walter,MORRELL S.Modelling fines in blast fragmentation and its impact on crushing and grinding[C]//Explo'99:A Conference on Rock Breaking.Kalgoorlie:AusIMM,1999,137-181".
2. IL' YUSHIN model, see "IL'YUSHIN A A.The mechanics ofa continuous medium[M].Moscow:Izd-vo MGU,1971.(In Russian)Translated in:HUSTRULID W.Blasting principles for open pit mining:Theoretical foundations[M].Rotterdam:Balkema,1999".
3. DJORDJEVIC model, see "DJORDJEVIC N.A two-component model of blast fragmentation[C]//The 6th International Symposium for Rock Fragmentation by Blasting(Fragblast-6).Johannesburg:SAIMM,1999,213-222".
4. SZULADZINSKI model, see "SZULADZINSKI G.Response ofrockmedium to explosive borehole pressure[C]//The Fourth International Symposium on Rock Fragmentation by Blasting(Fragblast-4).Vienna:Balkema,1993,17-23".
5. ESEN model, see "ESEN S,ONEDERRA I,BILGIN H A.Modelling the size ofthe crushed zone around a blasthole[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(4):485-495.DOI:10.1016/S1365-1609(03)00018-2".
6. Leng Zhendong model, see "Leng Zhendong, lu Wenbo, chen, et al, improvement of the rock drill burst shatter area calculation model [ J ]. Explosion and impact 2015,35 (1): 101-107".
7. Li Fangtao model, see "Li Fangtao, hu Zhiping, chen Nana, et al," method for calculating the range of tunnel surrounding rock fissures under blast load "study [ J ]. Vibration and impact, 2022,41 (8): 260-269".
The existing model has a certain limitation on the obtained theoretical formula due to different rock failure strength criteria, and the calculated result often has deviation from the actual value. The middle main stress and plastic damage of the surrounding rock can be considered by adopting the unified strength theory, so that the stress and damage state of the surrounding rock can be reflected better. Particularly for the practical drilling and blasting engineering of a deep-buried tunnel, the existing part of theoretical models have no practicability, and the influences of main stress, initial ground stress, initial damage, borehole cavity expansion, rock mass plastic damage and shear expansion characteristics in surrounding rock on the crack range of surrounding rock blasting damage are very remarkable. However, the current research on the fracture range of the surrounding rock blasting damage does not comprehensively consider the factors, and the influence mechanism of the principal stress and the ground stress on the fracture range is not clear.
Therefore, the development of the method and the equipment capable of effectively predicting the surrounding rock blasting damage fracture range has important significance.
Disclosure of Invention
The invention provides a surrounding rock blasting damage crack range prediction method which comprises the steps of obtaining working condition parameters, constructing a surrounding rock blasting damage crack range prediction model, then obtaining a surrounding rock damage partition crack range relational expression, and obtaining a surrounding rock blasting damage crack range based on the working condition parameters and the surrounding rock damage partition crack range relational expression. According to the prediction method, the characteristics of main stress, initial ground stress, initial damage, borehole cavity expansion, rock mass plastic damage and shear expansion in surrounding rock are comprehensively considered, and a control equation is established by using the unit displacement of the surrounding rock and the fracture radius, so that the theoretical analysis type of the calculation point stress displacement and the damage fracture radius of the surrounding rock of the deep buried tunnel based on the unified strength theory is obtained. The method can reveal the influence mechanism of initial ground stress and intermediate main stress on the range of surrounding rock blasting damage cracks, and effectively predict the range of cracks in the practical drilling and blasting engineering of the deep-buried tunnel while improving the blasting surrounding rock efficiency. The specific technical scheme is as follows:
A surrounding rock blasting damage crack range prediction method comprises the following steps:
acquiring working condition parameters, wherein the working condition parameters comprise explosive parameters, surrounding rock parameters and charging parameters;
Constructing a surrounding rock blasting damage fracture range prediction model to obtain a surrounding rock damage partition fracture range relation:
Wherein: r *m represents the maximum radius of the comminution zone, R Ⅰ represents the outer boundary extent of the fracture I zone, R Ⅱ represents the outer boundary extent of the fracture II zone, R b represents the borehole radius, a m represents the maximum radius of the cavity expansion, Represents a constant, sigma s represents the dynamic compressive strength of the rock mass under the condition of multidirectional stress, sigma c represents the uniaxial compressive strength of the surrounding rock, c t represents the uniform cohesive force,/>Representing the uniform internal friction angle, sigma td representing the dynamic tensile strength of the surrounding rock, sigma 0 representing the initial ground stress of the surrounding rock, and D 0 representing the initial damage factor of the surrounding rock;
and obtaining the surrounding rock blasting damage fracture range based on the relation between the working condition parameters and the surrounding rock damage partition fracture range.
Preferably, the explosive parameters comprise explosive density ρ 0, explosive explosion velocity D e, expansion heat index gamma 0, pressure increase coefficient n of expansion collision of explosion products on the wall of the gun hole, adiabatic index gamma 1, adiabatic index gamma 2 and critical explosion cavity pressure p k;
The parameters of the surrounding rock comprise initial ground stress sigma 0 of the surrounding rock, the density rho of the surrounding rock, the longitudinal wave speed C p of the surrounding rock, the medium principal stress coefficient B, the dynamic tensile strength sigma td of the surrounding rock, the initial damage factor D 0 of the surrounding rock, the uniaxial compressive strength sigma c of the surrounding rock, the cohesive force C and the internal friction angle Poisson's ratio μ, modulus E and surrounding shear expansion angle ψ;
the charging parameters comprise a gun hole radius r b, a gun hole charging uncoupling coefficient U and an axial charging coefficient l z.
Preferably, the construction of the surrounding rock blasting damage fracture range prediction model comprises the following steps:
The first step, construction of a stress equation, specifically comprises the following steps: obtaining a stress equation of an elastic zone, a stress equation of a fracture II zone, a stress equation of a fracture I zone and a stress equation of a crushing zone based on surrounding rock blasting damage partition characteristics, a stress balance differential equation, a radial stress boundary condition and a unified strength theory;
The construction of a radial displacement equation specifically comprises the following steps: describing the shear expansion characteristics of the surrounding rock in the plastic region by adopting a non-associated flow rule and a shear expansion angle based on the radial stress equation, the displacement balance differential equation and the displacement boundary condition in the first step to obtain a radial displacement equation of the elastic region, a radial displacement equation of the fracture II region, a radial displacement equation of the fracture I region and a radial displacement equation of the crushing region;
Thirdly, based on a radial stress equation in the first step and a radial displacement equation in the second step, according to a cavity wall expansion displacement control equation, combining an explosive detonation wave C-J theory and a two-stage Jonse-Miller adiabatic equation of blast hole cavity expansion to obtain a ratio of the maximum radius of the cavity expansion to the radius of the blast hole;
And fourthly, obtaining a surrounding rock fracture zone fracture range relation through a cavity wall displacement relation, a continuity condition of radial stress at the junction of the crushing zone and the fracture I zone and a fracture II zone radial stress equation based on the ratio of the maximum radius of the cavity expansion to the radius of the blast hole in the third step.
Preferably, in the first step: the stress equation for the elastic region is expressed as:
Wherein: Representing the radial stress of the elastic region,/> Representing the elastic zone hoop stress, R representing the calculated point location, σ Ⅱ representing the radial stress at the elastic zone inner boundary, i.e., r=r Ⅱ;
the radial stress equation for the fracture II zone is expressed as:
Wherein: the radial stress boundary condition of the fracture II zone is that Representing the radial stress at the outer boundary of the fracture ii region, i.e. r=r Ⅱ,/>Represents the radial stress at the outer boundary of the fracture i zone i.e. r=r Ⅰ,Representing the radial stress of the fracture II zone;
the stress equation for the fracture zone I is expressed as:
Wherein: the stress boundary condition of the fracture i zone is r=r Ⅰ, B represents the principal stress coefficient; Representing the radial stress of the fracture I zone,/> Represents the hoop stress of the fracture I zone;
The radial stress equation for the crush zone is expressed as:
Wherein: the stress boundary condition of the crushing zone is A represents the outer boundary range of the cavity region,/>Representing the radial stress at the outer boundary of the cavity region, i.e. r=a,/>Representing the radial stress of the crush zone, and R * represents the extent of the crush zone outer boundary.
Preferably, in the second step: the radial displacement equation for the elastic region is expressed as:
wherein: the radial stress displacement relation of the elastic region is Representing radial displacement of the elastic zone, w representing axial displacement, z representing the axial position of the calculation point, E representing the elastic modulus of the rock;
The radial displacement equation for the fracture II zone is expressed as:
wherein: the displacement boundary condition of the rupture zone II is that Representing the radial displacement at the outer boundary of the fracture ii region, i.e., r=r Ⅱ; the radial stress relation is sigma cRⅠ＝[σtd(1-D0)+2σ0]RⅡ; /(I)Representing the radial displacement of the fracture II zone;
The radial displacement equation for the fracture zone I is expressed as:
Wherein: Representing the radial displacement of the fracture zone I; a 0、A1、A2、A3、A4、A5 represents a constant, and a 0、A1、A2、A3、A4、A5 is respectively expressed as:
The radial displacement equation for the comminution zone is expressed as:
Wherein: representing the radial displacement of the comminution zone; η represents a scaling factor; r * represents the range of the outer boundary of the crushing zone.
Preferably, the radial displacement equation for the fracture zone I is obtained as follows:
the equation describing the shear and expansion characteristics of the surrounding rock in the fracture I area by adopting a non-associated flow rule and a shear and expansion angle is as follows:
Wherein: Representing radial plastic strain,/> Represents the hoop plastic strain;
The radial strain component and the circumferential strain component satisfy:
Wherein: epsilon r represents the radial total strain, epsilon θ represents the hoop total strain, Representing radial elastic strain,/>Represents the hoop elastic strain;
elastic strain is expressed by hooke's law as follows:
further, the radial displacement relation is obtained as follows:
The displacement boundary conditions are: Wherein/> Representing the radial displacement at the outer boundary of the fracture i region, i.e., r=r Ⅰ;
radial displacement equations for the fracture zone I were obtained.
Preferably, the third step specifically includes:
substituting r=a into the radial displacement equation of the crushing area obtained in the second step to obtain a cavity wall expansion displacement control equation as follows:
When the cavity expansion area reaches the maximum, namely a m, the crushing area is Expressed as:
wherein: a m represents the maximum radius of cavity expansion;
The initial impact pressure of the wall of the blast hole obtained by the detonation wave C-J theory of the explosive is as follows:
wherein: p represents the shock wave pressure;
The two-stage Jonse-Miller adiabatic equation for borehole cavity expansion is:
Wherein: r k is the critical explosion chamber radius corresponding to the critical explosion chamber pressure p k: p m represents the pressure on the cell wall when the cavity expansion reaches a maximum;
When the expansion area of the cavity is maximum, the radial stress of a calculation point on the wall surface is obtained based on the radial stress equation of the crushing area obtained in the first step, and is as follows:
Wherein: Representing the radial stress at the outer boundary of the cavity region, i.e., r=a m;
Obtaining an equation for solving the ratio (a m/rb) of the maximum radius of the cavity expansion to the radius of the blast hole:
Preferably, the fourth step specifically includes:
Based on the ratio of the maximum radius of the cavity expansion to the radius of the blast hole obtained in the third step, determining the relationship between the maximum radius of the crushing area and the maximum radius of the cavity expansion as follows:
the continuity condition of radial stress at the junction of the crushing zone and the fracture zone I is as follows:
and combining the radial stress equation of the fracture II area to obtain a relational expression of the fracture range of the surrounding rock fracture zone.
The invention also discloses a storage medium which stores a computer program, wherein the computer program is suitable for being loaded by a processor and executing the surrounding rock blasting damage fracture range prediction method.
The invention also discloses equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the computer program runs the surrounding rock blasting damage fracture range prediction method when being executed by the processor.
Drawings
In order to more clearly illustrate exemplary embodiments of the present application, the drawings required in the examples will be briefly described below. It is to be understood that the drawings are designed to aid in the further understanding of embodiments of the application and are not to be construed as limiting the application, together with the description of embodiments of the application.
FIG. 1 is a flow chart of a method for predicting a range of a surrounding rock blasting damage fracture provided by an embodiment of the application;
FIG. 2 is a schematic diagram showing the stress state of surrounding rock units in the range of the action of explosion shock waves in the embodiment of the application;
FIG. 3 is a schematic diagram of a surrounding rock borehole blasting failure zone in accordance with an embodiment of the present application;
FIG. 4 is a graph showing the range of fracture damage due to surrounding rock blasting with initial stress change in accordance with an embodiment of the present application, wherein: FIG. 4 (a) shows the fracture range in the crush zone; FIG. 4 (b) shows the fracture zone I crack extent; FIG. 4 (c) shows the fracture zone II;
FIG. 5 is a graph showing the range of surrounding rock blast damage fractures as a function of the median principal stress coefficient in an embodiment of the application, wherein: FIG. 5 (a) shows the fracture range in the crush zone; FIG. 5 (b) shows the fracture zone I crack extent; FIG. 5 (c) shows the fracture zone II;
FIG. 6 is a comparison of the results of predicting the extent of crush zone for the protocol of this example with KANCHIBOTLA model, IL' YUSHIN model, DJORDJEVIC model, SZULADZINSKI model and ESEN model, based on the extent of crush zone obtained in the prior 12-group blast test;
FIG. 7 is a graph showing the fracture I zone range prediction results of the present example against numerical simulations, leng Zhendong models and Li Fangtao models based on the fracture I zone range obtained in the 1-group blasting test.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It is noted that unless otherwise indicated, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this application belongs.
Examples
The embodiment provides a surrounding rock blasting damage fracture range prediction method, and the method is described below with reference to the accompanying drawings.
Referring to fig. 1, a flowchart of a method for predicting a range of a fracture of a surrounding rock blasting damage according to some embodiments of the present application is shown, which specifically includes the following steps:
Step one, acquiring working condition parameters, wherein the working condition parameters comprise explosive parameters, surrounding rock parameters and charging parameters.
The preferred embodiment is: the explosive parameters comprise explosive density rho 0, explosive explosion speed D e, expansion heat index gamma 0, pressure increase coefficient n of expansion collision of explosion products on the wall of a gun hole, heat insulation index gamma 1, heat insulation index gamma 2 and critical explosion cavity pressure p k; the parameters of the surrounding rock comprise initial ground stress sigma 0, surrounding rock density rho, longitudinal wave speed C p, medium principal stress coefficient B, dynamic tensile strength sigma td, initial damage factor D 0, uniaxial compressive strength sigma c, cohesive force C and internal friction angle of the surrounding rockPoisson's ratio μ, modulus E and surrounding shear expansion angle ψ; the charging parameters comprise a gun hole radius r b, a gun hole charging uncoupling coefficient U and an axial charging coefficient l z.
Step two, constructing a surrounding rock blasting damage fracture range prediction model to obtain a surrounding rock damage partition fracture range relation, wherein the method specifically comprises the following steps:
The first step, construction of a stress equation, specifically comprises the following steps: obtaining a stress equation of an elastic zone, a stress equation of a fracture II zone, a stress equation of a fracture I zone and a stress equation of a crushing zone based on surrounding rock blasting damage partition characteristics, a stress balance differential equation, a radial stress boundary condition and a unified strength theory;
The construction of a radial displacement equation specifically comprises the following steps: describing the shear expansion characteristics of the surrounding rock in the plastic region by adopting a non-associated flow rule and a shear expansion angle based on the radial stress equation, the displacement balance differential equation and the displacement boundary condition in the first step to obtain a radial displacement equation of the elastic region, a radial displacement equation of the fracture II region, a radial displacement equation of the fracture I region and a radial displacement equation of the crushing region;
Thirdly, based on a radial stress equation in the first step and a radial displacement equation in the second step, according to a cavity wall expansion displacement control equation, combining an explosive detonation wave C-J theory and a two-stage Jonse-Miller adiabatic equation of blast hole cavity expansion to obtain a ratio of the maximum radius of the cavity expansion to the radius of the blast hole;
And fourthly, obtaining a surrounding rock fracture zone fracture range relation through a cavity wall displacement relation, a continuity condition of radial stress at the junction of the crushing zone and the fracture I zone and a fracture II zone radial stress equation based on the ratio of the maximum radius of the cavity expansion to the radius of the blast hole in the third step.
Preferred in this embodiment are:
1) The stress equation for the elastic region is expressed as:
Wherein: Representing the radial stress of the elastic zone, σ 0 being the initial ground stress of the surrounding rock, R Ⅱ being the outer boundary range of the fracture ii zone, R representing the calculated point location, σ Ⅱ representing the inner boundary of the elastic zone, i.e. the radial stress at r=r Ⅱ,/> Indicating the hoop stress of the elastic region.
2) The stress equation for the fracture I zone is obtained as follows:
the fracture II zone radial stress boundary conditions include:
the radial stress equation for the fracture II zone is expressed as:
Wherein: r Ⅱ is the outer boundary range of the rupture II region, R Ⅰ is the outer boundary range of the rupture I region, Represents the radial stress at the outer boundary of the fracture ii zone, i.e. r=r Ⅱ, σ td represents the dynamic tensile strength of the surrounding rock, D 0 represents the initial damage factor of the surrounding rock, σ 0 is the initial ground stress of the surrounding rock,/>Represents the radial stress at the outer boundary of the fracture I zone, i.e. r=R Ⅰ, σ c represents the uniaxial compressive strength of the surrounding rock,/>Representing the radial stress of the fracture ii zone, σ td represents the dynamic tensile strength of the surrounding rock.
3) The stress equation for the fracture I zone is obtained as follows:
the stress boundary conditions for the rupture zone I include:
Uniform internal friction angle And the uniform cohesion c t is expressed as:
Wherein: c represents the cohesive force of the adhesive tape, The internal friction angle is represented, and B represents the principal stress coefficient in the middle;
The fracture I zone stress equation is expressed as:
Wherein, Representing the radial stress of the fracture I zone,/>Representing the hoop stress of the fracture zone i.
4) The radial stress equation of the crushing zone is obtained as follows:
The stress boundary conditions of the crushing zone are as follows:
the crushing zone radial stress equation is expressed as:
Wherein: a represents the outer boundary extent of the cavity region, Representing the radial stress at the outer boundary of the cavity region, i.e. r=a,/>Representing radial stress of a crushing zone, R * representing the outer boundary range of the crushing zone, sigma s representing dynamic compressive strength of the rock mass under the condition of multidirectional stress, ρ representing surrounding rock density, and C p representing surrounding rock longitudinal wave velocity.
In this embodiment, preferably, the radial stress displacement relation of the elastic region obtained based on the radial stress equation in the first step in the second step is:
Wherein θ is:
Wherein: Represents the radial stress of the elastic region, μ represents the Poisson's ratio of rock, E represents the elastic modulus of rock, r represents the calculated point location,/> Represents the radial displacement of the elastic zone, w represents the axial displacement, and z represents the axial position of the calculation point. /(I)
Considering that natural rock mass has an initial damage factor (D 0 represents the initial damage factor of surrounding rock), the elastic zone radial displacement equation is expressed as:
wherein: r Ⅱ represents the outer boundary extent of the fracture II zone, σ td represents the dynamic tensile strength of the surrounding rock, and σ 0 represents the initial ground stress of the surrounding rock.
The rupture zone II displacement boundary conditions are:
Wherein, Representing the radial displacement at the outer boundary of the fracture ii region, i.e. r=r Ⅱ.
The radial stress relationship is:
σcRⅠ＝[σtd(1-D0)+2σ0]RⅡ；
Wherein R Ⅰ represents the fracture I zone outer boundary range, and σ c represents the uniaxial compressive strength of the surrounding rock.
The fracture II zone radial displacement equation is expressed as:
Wherein: representing the radial displacement of the fracture ii zone.
The equation describing the shear and expansion characteristics of the surrounding rock in the fracture I area by adopting a non-associated flow rule and a shear and expansion angle is as follows:
Wherein: Representing radial plastic strain,/> Represents the hoop plastic strain;
The radial strain component and the circumferential strain component satisfy:
Wherein: ψ represents the surrounding rock shear angle, ε r represents the radial total strain, ε θ represents the hoop total strain, Representing radial elastic strain,/>Representing the elastic strain in the circumferential direction,/>Representing the radial displacement of the fracture zone i.
Elastic strain is expressed by hooke's law as follows:
/>
Further, the radial displacement relation can be obtained as follows:
Wherein A 0、A1 is represented by:
The displacement boundary conditions are:
Wherein/> Representing the radial displacement at the outer boundary of the fracture i region, i.e., r=r Ⅰ;
Wherein A2 is represented by:
Wherein, Represents the radial displacement at the outer boundary of the fracture i zone, i.e. r=r Ⅰ.
The fracture zone I radial displacement equation is expressed as:
Wherein A 3、A4、A5 is represented by:
Wherein, Representing the radial displacement of the fracture I zone, A 0、A1、A2、A3、A4、A5 represents a constant.
The radial stress continuity conditions on the outer boundary of the crushing zone are as follows:
wherein R * represents the range of the outer boundary of the crushing zone, and η represents the proportionality coefficient.
The displacement boundary conditions of the crushing zone are as follows:
Wherein, The radial displacement of the outer boundary of the crushing zone, i.e. r=r *, is indicated.
The crushing zone radial displacement equation is expressed as:
Wherein, Representing the radial displacement of the comminution zone.
Specifically, in the third step in the second step, r=a is substituted into the radial displacement equation of the crushing area obtained in the second step, and the cavity wall expansion displacement control equation is as follows:
When the cavity expansion area reaches the maximum, namely a m, the crushing area is Represented by formula (1):
Wherein a m denotes the maximum radius of expansion of the cavity, Indicating the maximum radius of the comminution zone.
The initial impact pressure of the wall of the blast hole obtained by the detonation wave C-J theory of the explosive is as follows:
Wherein p represents the pressure of the shock wave, ρ represents the density of surrounding rock, ρ 0 represents the density of explosive, D e represents the detonation velocity of the explosive, C p represents the longitudinal wave velocity of the surrounding rock, gamma 0 represents the expansion heat index, U represents the uncoupled coefficient of charge of the blast hole, n represents the pressure increase coefficient of expansion collision of the explosion product on the wall of the blast hole, and l z represents the axial charge coefficient.
The two-stage Jonse-Miller adiabatic equation for borehole cavity expansion is:
Wherein: p m represents the pressure on the hole wall when the cavity expansion reaches the maximum, r k is the critical explosion cavity radius corresponding to the critical explosion cavity pressure p k, and the expression is:
When the expansion area of the cavity is maximum, based on the radial stress equation of the crushing area obtained in the first step, the radial stress of the calculated point on the wall surface can be obtained as follows:
Wherein: The radial stress at the outer boundary of the cavity region, i.e., r=a m, is indicated.
Combined formula (3), (5) and formula (7), yields:
The ratio a m/rb of the maximum radius of the expansion of the cavity to the radius of the blast hole can be obtained by the formula (8).
Specifically, in the fourth step in the second step, based on the ratio of the maximum radius of the expansion of the cavity to the radius of the blast hole obtained in the third step, the relationship between the maximum radius of the crushing area and the maximum radius of the expansion of the cavity is determined as follows:
the continuity condition of radial stress at the junction of the crushing zone and the fracture zone I is as follows:
The relation formula for obtaining the fracture range of the surrounding rock fracture zone by combining the radial stress equation of the fracture II zone is as follows:
And thirdly, obtaining a prediction result based on the relation between the working condition parameters and the surrounding rock damage partition fracture range, and obtaining the surrounding rock blasting damage fracture range.
The present embodiment also provides a storage medium storing a computer program adapted to be loaded by a processor and to perform the above-described method of predicting a range of a surrounding rock blast damage fracture.
The embodiment also provides equipment, which comprises a memory and a processor, wherein the memory stores a computer program, and the computer program runs the surrounding rock blasting damage fracture range prediction method when the computer program is executed by the processor.
As shown in fig. 2, under the action of blasting load, the actual surrounding rock unit body is respectively subjected to radial stress sigma r, circumferential stress sigma θ and axial stress sigma z, the traditional model usually ignores the middle main stress, so that the stress of the computing model deviates from the actual rock body, and the three main stresses are comprehensively considered based on the unified strength theory.
As shown in fig. 3, under initial ground stress, the surrounding rock caused by the borehole blasting breaks the zone range. Surrounding rocks near the blastholes bear severe impact pressure from inside to outside, so that fracture rings are formed outside the primary support of the tunnel. The traditional surrounding rock blasting damage areas are a crushing area, a cracking area and an elastic area. The calculation model adopted by the invention divides the fracture zone in the traditional model into a fracture zone I and a fracture zone II, specifically, the surrounding rock of the fracture zone I is considered to be completely destroyed, the surrounding rock of the fracture zone I comprises plastic destruction and has a large number of microscopic cracks and circumferential bearing capacity, the surrounding rock of the fracture zone II is completely penetrated by radial cracks and loses the circumferential bearing capacity, and the division limit of the fracture zone I and the fracture zone II is the distribution density of the cracks. According to the method, main stress, initial ground stress, initial damage, borehole cavity expansion, rock mass plastic damage and shear expansion characteristics in surrounding rock are comprehensively considered, so that point stress displacement and damage fracture radius theoretical analysis type surrounding rock calculation points of the deep-buried tunnel based on a unified strength theory are established, and the trend that the surrounding rock blasting damage fracture range changes along with the initial ground stress and the medium main stress coefficient is obtained, as shown in fig. 4 and 5.
As shown in fig. 6, the technical scheme of this example was compared with the result of predicting the crushing zone range of KANCHIBOTLA model, IL' YUSHIN model, DJORDJEVIC model, SZULADZINSKI model and ESEN model according to the crushing zone range obtained in the conventional 12-group blasting test. As can be seen from fig. 6, the predicted radius of the technical solution of the present embodiment is closer to the experimental measurement radius than the predicted radius of the existing model, so that the effectiveness and superiority of the technical solution of the present embodiment in predicting the range of the broken rock area can be illustrated.
As shown in FIG. 7, the technical scheme of the present example was compared with the results of numerical simulation, leng Zhendong model and Li Fangtao model for predicting the fracture I zone fracture range according to the fracture I zone fracture range obtained in the 1-group blasting test. As can be seen from fig. 7, the fracture radius of the fractured i zone obtained by the technical solution of this embodiment is closer to the test results than the numerical simulation, leng Zhendong model and Li Fangtao model, so that the effectiveness and superiority of the technical solution of this embodiment in predicting the fractured i zone of the blasted rock can be illustrated.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the application, and are intended to be included within the scope of the appended claims and description.
Claims (10)
1. The method for predicting the range of the surrounding rock blasting damage fracture is characterized by comprising the following steps:
acquiring working condition parameters, wherein the working condition parameters comprise explosive parameters, surrounding rock parameters and charging parameters;
Constructing a surrounding rock blasting damage fracture range prediction model to obtain a surrounding rock damage partition fracture range relation:
Wherein: r *m represents the maximum radius of the comminution zone, R Ⅰ represents the outer boundary extent of the fracture I zone, R Ⅱ represents the outer boundary extent of the fracture II zone, R b represents the borehole radius, a m represents the maximum radius of the cavity expansion, Represents a constant, sigma s represents the dynamic compressive strength of the rock mass under the condition of multidirectional stress, sigma c represents the uniaxial compressive strength of the surrounding rock, c t represents the uniform cohesive force,/>Representing the uniform internal friction angle, sigma td representing the dynamic tensile strength of the surrounding rock, sigma 0 representing the initial ground stress of the surrounding rock, and D 0 representing the initial damage factor of the surrounding rock;
and obtaining the surrounding rock blasting damage fracture range based on the relation between the working condition parameters and the surrounding rock damage partition fracture range.
2. The method for predicting the range of surrounding rock blasting damage and fissures according to claim 1, wherein the explosive parameters comprise an explosive density ρ 0, an explosive explosion velocity D e, an expansion heat index γ 0, a pressure increase coefficient n of an explosion product expanding and impacting a wall of a blast hole, an adiabatic index γ 1, an adiabatic index γ 2 and a critical explosion cavity pressure p k;
The parameters of the surrounding rock comprise initial ground stress sigma 0 of the surrounding rock, the density rho of the surrounding rock, the longitudinal wave speed C p of the surrounding rock, the medium principal stress coefficient B, the dynamic tensile strength sigma td of the surrounding rock, the initial damage factor D 0 of the surrounding rock, the uniaxial compressive strength sigma c of the surrounding rock, the cohesive force C and the internal friction angle Poisson's ratio μ, modulus E and surrounding shear expansion angle ψ;
the charging parameters comprise a gun hole radius r b, a gun hole charging uncoupling coefficient U and an axial charging coefficient l z.
3. The method for predicting the range of a surrounding rock blasting damage fracture according to claim 2, wherein constructing the model for predicting the range of the surrounding rock blasting damage fracture comprises the steps of:
The first step, construction of a stress equation, specifically comprises the following steps: obtaining a stress equation of an elastic zone, a stress equation of a fracture II zone, a stress equation of a fracture I zone and a stress equation of a crushing zone based on surrounding rock blasting damage partition characteristics, a stress balance differential equation, a radial stress boundary condition and a unified strength theory;
The construction of a radial displacement equation specifically comprises the following steps: describing the shear expansion characteristics of the surrounding rock in the plastic region by adopting a non-associated flow rule and a shear expansion angle based on the radial stress equation, the displacement balance differential equation and the displacement boundary condition in the first step to obtain a radial displacement equation of the elastic region, a radial displacement equation of the fracture II region, a radial displacement equation of the fracture I region and a radial displacement equation of the crushing region;
Thirdly, based on a radial stress equation in the first step and a radial displacement equation in the second step, according to a cavity wall expansion displacement control equation, combining an explosive detonation wave C-J theory and a two-stage Jonse-Miller adiabatic equation of blast hole cavity expansion to obtain a ratio of the maximum radius of the cavity expansion to the radius of the blast hole;
And fourthly, obtaining a surrounding rock fracture zone fracture range relation through a cavity wall displacement relation, a continuity condition of radial stress at the junction of the crushing zone and the fracture I zone and a fracture II zone radial stress equation based on the ratio of the maximum radius of the cavity expansion to the radius of the blast hole in the third step.
4. A method for predicting the range of a surrounding rock blast damage fracture according to claim 3, wherein in the first step:
The stress equation for the elastic region is expressed as:
Wherein: Representing the radial stress of the elastic region,/> Representing the elastic zone hoop stress, R representing the calculated point location, σ Ⅱ representing the radial stress at the elastic zone inner boundary, i.e., r=r Ⅱ;
the radial stress equation for the fracture II zone is expressed as:
Wherein: the radial stress boundary condition of the fracture II zone is that Representing the radial stress at the outer boundary of the fracture ii region, i.e. r=r Ⅱ,/>Representing the radial stress at the outer boundary of the fracture I zone, i.e. r=R Ⅰ,/>Representing the radial stress of the fracture II zone;
the stress equation for the fracture zone I is expressed as:
Wherein: the stress boundary condition of the fracture i zone is r=r Ⅰ, B represents the principal stress coefficient; Representing the radial stress of the fracture I zone,/> Represents the hoop stress of the fracture I zone;
The radial stress equation for the crush zone is expressed as:
Wherein: the stress boundary condition of the crushing zone is A represents the outer boundary range of the cavity region,/>Representing the radial stress at the outer boundary of the cavity region, i.e. r=a,/>Representing the radial stress of the crush zone, and R * represents the extent of the crush zone outer boundary.
5. The method for predicting the range of a surrounding rock blast damage fracture according to claim 4, wherein in the second step:
The radial displacement equation for the elastic region is expressed as:
wherein: the radial stress displacement relation of the elastic region is Representing radial displacement of the elastic zone, w representing axial displacement, z representing the axial position of the calculation point, E representing the elastic modulus of the rock;
The radial displacement equation for the fracture II zone is expressed as:
wherein: the displacement boundary condition of the rupture zone II is that Representing the radial displacement at the outer boundary of the fracture ii region, i.e., r=r Ⅱ; the radial stress relation is sigma cRⅠ＝[σtd(1-D0)+2σ0]RⅡ; /(I)Representing the radial displacement of the fracture II zone;
The radial displacement equation for the fracture zone I is expressed as:
Wherein: Representing the radial displacement of the fracture zone I; a 0、A1、A2、A3、A4、A5 represents a constant, and a 0、A1、A2、A3、A4、A5 is respectively expressed as:
The radial displacement equation for the comminution zone is expressed as:
Wherein: representing the radial displacement of the comminution zone; η represents a scaling factor; r * represents the range of the outer boundary of the crushing zone.
6. The method for predicting the range of a surrounding rock blasting damage fracture according to claim 5, wherein,
The radial displacement equation for the fracture zone I is obtained as follows:
the equation describing the shear and expansion characteristics of the surrounding rock in the fracture I area by adopting a non-associated flow rule and a shear and expansion angle is as follows:
Wherein: Representing radial plastic strain,/> Represents the hoop plastic strain;
The radial strain component and the circumferential strain component satisfy:
Wherein: epsilon r represents the radial total strain, epsilon θ represents the hoop total strain, Representing radial elastic strain,/>Represents the hoop elastic strain;
elastic strain is expressed by hooke's law as follows:
further, the radial displacement relation is obtained as follows:
The displacement boundary conditions are: Wherein/> Representing the radial displacement at the outer boundary of the fracture i region, i.e., r=r Ⅰ;
radial displacement equations for the fracture zone I were obtained.
7. The method for predicting the range of a surrounding rock blast damage fracture according to claim 6, wherein the third step specifically comprises:
substituting r=a into the radial displacement equation of the crushing area obtained in the second step to obtain a cavity wall expansion displacement control equation as follows:
when the cavity expansion region reaches a maximum, a m, there is a crush region R *m, expressed as:
wherein: a m represents the maximum radius of cavity expansion;
The initial impact pressure of the wall of the blast hole obtained by the detonation wave C-J theory of the explosive is as follows:
wherein: p represents the shock wave pressure;
The two-stage Jonse-Miller adiabatic equation for borehole cavity expansion is:
Wherein: r k is the critical explosion chamber radius corresponding to the critical explosion chamber pressure p k: p m represents the pressure on the cell wall when the cavity expansion reaches a maximum;
When the expansion area of the cavity is maximum, the radial stress of a calculation point on the wall surface is obtained based on the radial stress equation of the crushing area obtained in the first step, and is as follows:
Wherein: Representing the radial stress at the outer boundary of the cavity region, i.e., r=a m;
Obtaining an equation for solving the ratio (a m/rb) of the maximum radius of the cavity expansion to the radius of the blast hole:
8. The method for predicting the range of a surrounding rock blast damage fracture according to claim 7, wherein the fourth step specifically comprises:
Based on the ratio of the maximum radius of the cavity expansion to the radius of the blast hole obtained in the third step, determining the relationship between the maximum radius of the crushing area and the maximum radius of the cavity expansion as follows:
the continuity condition of radial stress at the junction of the crushing zone and the fracture zone I is as follows:
and combining the radial stress equation of the fracture II area to obtain a relational expression of the fracture range of the surrounding rock fracture zone.
9. A storage medium storing a computer program adapted to be loaded by a processor and to perform the method of surrounding rock blast damage fracture range prediction according to any one of claims 1 to 8.
10. An apparatus comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, operates the method of predicting the range of a surrounding rock blast damage fracture of any one of claims 1-8.
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| CN116913416A (en) * | 2023-09-12 | 2023-10-20 | 中国地质大学（北京） | Quantitative evaluation and prediction method and device for weathering degree of sea rock |
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| CN117053645A (en) * | 2023-06-27 | 2023-11-14 | 中交一公局集团有限公司 | Layered slope precise blasting construction method |
| CN116913416A (en) * | 2023-09-12 | 2023-10-20 | 中国地质大学（北京） | Quantitative evaluation and prediction method and device for weathering degree of sea rock |
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