A method for analyzing and predicting the fragmentation of ore blasting

Abstract

The present invention relates to the technical field of ore fragmentation analysis, and specifically to a method for analyzing and predicting ore blasting fragmentation. Clarify the friction angle and cohesion affected by the wetting effect and freeze-thaw effect in weather conditions; determine the friction angle correction parameter and cohesion correction parameter in the Drucker-Prager model based on the friction angle and cohesion and substitute them into the yield function to determine whether the rock mass yields and whether the current rock mass is broken or separated; establish a dynamic equation through the finite element method to clarify the dynamic response of the rock mass under blasting load and environmental loading; determine whether the rock mass is damaged and cracks are generated under stress based on the crack extension criterion, and predict the blasting fragmentation based on the rock mass cracks. Based on the Drucker-Prager model, the rock mass strength parameters are corrected by introducing the wetting effect and freeze-thaw effect, and the blasting dynamics equation is established in combination with the finite element method to predict the dynamic response of the rock mass under blasting load and environmental loading and the crack extension mode, thereby improving the current prediction accuracy of mine blasting fragmentation.

Description

Technical Field

[0001] The invention relates to the technical field of ore fragmentation analysis, and in particular to a method for analyzing and predicting ore blasting fragmentation. Background Art

[0002] Mine blasting is a core step in mining engineering. Its goal is to break the rock into a size range suitable for subsequent processing. The size distribution has a direct impact on subsequent transportation, crushing efficiency and economic cost.

[0003] However, the mechanical behavior of rock mass is affected by many factors, including blasting design parameters (such as charge amount, detonation sequence, etc.), rock mass properties (such as strength, joint and fissure distribution) and external environment (such as rainfall and snowfall). Especially in areas with complex weather conditions, wetting effect and freeze-thaw effect may significantly change the strength and crack extension mode of rock mass, thus affecting the fragmentation distribution.

[0004] Traditional blasting size prediction methods are usually based on experience or statistical models, and fail to fully consider the dynamic impact of weather factors on rock mechanical properties and blasting effects. This neglect will lead to insufficient prediction accuracy of blasting size and cannot meet the needs of mine blasting design optimization in complex environments. Summary of the invention

[0005] In view of the above-mentioned shortcomings of the prior art, the present invention provides a method for analyzing and predicting the blasting fragmentation of ore, which can effectively solve the problem that the prior art fails to fully consider the dynamic influence of weather factors on the mechanical properties of rock mass and blasting effect, thereby affecting the accuracy of blasting fragmentation prediction.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0007] The present invention provides a method for analyzing and predicting the blasting fragmentation of an ore, comprising the following steps:

[0008] The weather state is introduced into the Drucker-Prager model to clarify the friction angle and cohesion affected by the wetting effect and freeze-thaw effect in the weather state;

[0009] According to the friction angle and cohesion, the friction angle correction parameter and cohesion correction parameter in the Drucker-Prager model are determined and substituted into the yield function to determine whether the rock mass has yielded and whether the current rock mass is broken or separated.

[0010] The dynamic equation is established by the finite element method to clarify the dynamic response of the rock mass under blasting load and environmental load, where:

[0011] The expression of the dynamic equation is:

[0012]

[0013] in, represents the mass matrix, represents the damping matrix, represents the stiffness matrix of the rock mass, represents the acceleration vector, represents the velocity vector, represents the displacement vector, represents the external load vector, represents additional force;

[0014] Based on the crack extension criterion, it is judged whether the rock mass is damaged and cracks are generated under stress, and the blasting block size is predicted based on the rock mass cracks.

[0015] Furthermore, the friction angle and cohesion affected by the wetting effect and the freeze-thaw effect are determined according to the following relationship:

[0016]

[0017] in, and They represent the friction angle and cohesion of the rock mass after being affected by the wetting effect and the freeze-thaw effect, respectively. represent the initial friction angle and cohesion respectively, and They represent the attenuation sensitivity coefficients of crack density to friction angle and cohesion respectively, represents the density of joints and cracks, and are the attenuation sensitivity coefficients of pore pressure to friction angle and cohesion, respectively. Represents the pore pressure.

[0018] Furthermore, the method for judging whether the rock mass has yielded is:

[0019] The parameters of the Drucker-Prager model are determined based on the friction angle and cohesion under the wetting effect and freeze-thaw effect, and then:

[0020]

[0021] in, represents the friction angle correction parameter in the Drucker-Prager model, represents the cohesion correction parameter in the Drucker-Prager model;

[0022] Introducing the friction angle correction parameter and the cohesion correction parameter into the Drucker-Prager yield function, it is determined whether the rock mass yields under a given stress state, and then:

[0023]

[0024] in, represents the value of the Drucker-Prager yield function, represents the stress tensor, represents the first invariant under the stress tensor, represents the second invariant of the deviatoric stress tensor;

[0025] Among them, if When it is 0, the rock mass is judged to be in a yield state.

[0026] Furthermore, the second invariant The solution is:

[0027]

[0028] in, is the deviatoric stress tensor Quantity;

[0029]

[0030] in, The total stress tensor is Quantity, Kronecker symbol.

[0031] Furthermore, the steps of establishing dynamic equations by finite element method to clarify the dynamic response of rock mass under blasting load and environmental loading are as follows:

[0032] Establish a finite element model, determine the geometric dimensions of the rock mass and blasting area according to the actual mining conditions, and perform geometric modeling;

[0033] assigning updated rock mass strength parameters to each material unit volume;

[0034] Divide the mine area into grids. The steps of grid division include:

[0035] Select the mesh type, including tetrahedral elements, hexahedral elements, triangular elements, or quadrilateral elements;

[0036] Set the mesh density;

[0037] Set boundary conditions and initial conditions, including:

[0038] Dynamic temperature field boundary conditions, freeze-thaw effect through temperature If the change of affects the rock mass, then we have

[0039]

[0040] in, represents the temperature at time t, represents the initial temperature, represents the temperature attenuation coefficient;

[0041] Dynamic humidity field boundary conditions, humidification effect through pore pressure If the change of affects the rock mass strength, then we have:

[0042] The diffusion of humidity field is based on the diffusion equation:

[0043]

[0044] in, represents the water saturation of the rock mass, represents the rate of change of saturation over time, represents the temperature diffusion coefficient, Indicates the rate of change of saturation in space;

[0045] Humidity loading boundary, rainfall Convert to saturation:

[0046]

[0047] in, represents the initial saturation, It represents the conversion coefficient of rainfall to saturation, describing the effect of unit rainfall on saturation;

[0048] Initial conditions, set to the rock mass state at the beginning of wetting and freeze-thaw, include:

[0049] Initial temperature field: preset the initial temperature distribution of the rock mass;

[0050] Initial humidity field: through the initial saturation set up;

[0051] The dynamic equations are formulated and solved by the central difference method.

[0052] Furthermore, the external load vector The method to determine is:

[0053] The blasting load changes dynamically, then:

[0054]

[0055] in, represents the blasting load at time t, represents the initial blasting load, represents the pressure wave attenuation coefficient, where:

[0056] Apply the blasting load to obtain the external load vector , then:

[0057]

[0058] in, Indicates the area of ​​action.

[0059] Furthermore, the additional force According to the following relationship:

[0060]

[0061] in, represents the volume of a finite element unit in the rock mass, represents the strain-displacement matrix, represents the transpose of the strain-displacement matrix, Represents a unit volume element.

[0062] The stiffness matrix The solution is:

[0063]

[0064] in, represents the stiffness matrix, represents the initial stiffness, represents the temperature sensitivity coefficient, Represents the temperature field.

[0065] Furthermore, the crack extension criterion determines whether the rock mass is damaged and cracks are generated under stress:

[0066]

[0067] in, represents the shear stress, represents the normal stress, represents the tangent of the friction angle, represents the friction angle, It indicates cohesion;

[0068] like , it means that the rock mass is damaged and the cracks begin to expand. Indicates shear strength.

[0069] Furthermore, the method for predicting the blasting size is:

[0070] Define fragmentation based on fracture geometry ;

[0071] Using the Rosin-Rammler distribution description, we have,

[0072]

[0073] in, Indicates that the particle size is smaller than The block ratio of , It represents the characteristic particle size and the scale parameter of the block size distribution. Represents the distribution index.

[0074] Compared with the known prior art, the technical solution provided by the present invention has the following beneficial effects:

[0075] Based on the Drucker-Prager model, the rock strength parameters were corrected by introducing the wetting effect and freeze-thaw effect. The blasting dynamics equation was established in combination with the finite element method to predict the dynamic response and crack propagation mode of the rock mass under blasting load and environmental loading, thereby improving the current prediction accuracy of mine blasting fragmentation. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0077] Figure 1 It is a schematic diagram of the overall method of the present invention. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] The present invention will be further described below in conjunction with the embodiments.

[0080] Example 1 (see Figure 1 ): A method for analyzing and predicting the size of ore blasting fragmentation, comprising at least:

[0081] Step 1: Conduct preliminary analysis of the yield of the mine rock mass to determine whether the rock mass has cracked or separated, including:

[0082] The weather state is combined with the Drucker-Prager model to define the mine rock material model (elastic-plastic behavior of the rock mass). The weather state includes rainfall and snowfall. The effects of rainfall and snowfall on the rock mass include:

[0083] Wetting effect of rock mass: Rainfall or snowfall penetrates into the rock mass, causing changes in the pore pressure of the rock mass by increasing the amount of water, thereby reducing cohesion and changing the friction angle;

[0084] Wetting-induced cracks: increase the slip of rock joints and reduce shear strength;

[0085] Freeze-thaw effect of rock mass: After water freezes and expands inside the rock mass, the subsequent melting process will change the pore structure and crack characteristics of the rock mass, causing the cracks to expand and affect the strength of the rock mass;

[0086] Therefore, the influence of freeze-thaw effect on crack density is defined (freeze-thaw effect changes the density of joint cracks by The sliding characteristics between the cracks (friction angle, cohesion) affect the strength of the rock mass), then:

[0087]

[0088] in, represents the initial joint density, represents the incremental coefficient of freeze-thaw effect on crack density, represents the number of freeze-thaw cycles;

[0089] Calculate the effect of freeze-thaw effects on the friction angle and cohesion:

[0090]

[0091] in, represents the friction angle after freeze-thaw effect, represents the cohesion after freeze-thaw effect, represent the initial friction angle and cohesion respectively, and are the attenuation sensitivity coefficients of crack density to friction angle and cohesion, respectively. Represents the density of joints and cracks.

[0092] Define the influence of wetting effect on rock mass strength (wetting mainly acts by changing the friction angle and cohesion Affects rock mass strength), then:

[0093]

[0094] in, represents the friction angle after wetting effect, represents the cohesion after the wetting effect, and are the attenuation sensitivity coefficients of pore pressure to friction angle and cohesion, respectively. represents the pore pressure as a function of the effect of rain and snow, where:

[0095]

[0096] in, represents the rock mass permeability coefficient, Indicates the water saturation in the rock mass.

[0097] Furthermore, after integrating the wetting effect and freeze-thaw effect, the rock strength parameters (friction angle and cohesion) are:

[0098]

[0099] in, and They represent the friction angle and cohesion of the rock mass after being affected by the wetting effect and the freeze-thaw effect, respectively. are the initial friction angle and cohesion, respectively. Under the action of wetting and freeze-thaw effects, the changes in cohesion and friction angle will directly affect the yield criterion, thereby affecting the yield behavior of the rock mass. In this way, the Drucker-Prager model parameters can be further determined by the friction angle and cohesion after the wetting effect and freeze-thaw effect:

[0100]

[0101] in, It represents the friction angle correction parameter in the Drucker-Prager model, reflecting the influence of wetting effect and freeze-thaw effect on the shape of the yield surface. It represents the cohesion correction parameter in the Drucker-Prager model, which is affected by the combined effects of wetting and freeze-thaw.

[0102] Based on the friction angle correction parameters and cohesion correction parameters defined above, the combination with weather conditions can be substituted into the Drucker-Prager yield function to determine whether the rock mass yields under a given stress state. Then, we have:

[0103]

[0104] in, represents the Drucker-Prager yield function value, describing the yield condition of rock mass material. If it is 0, it means that the rock mass is in a yield state. represents the stress tensor, represents the first invariant under the stress tensor, represents the sum of the principal stresses, represents the second invariant of the deviatoric stress tensor, reflecting the total magnitude of the deviatoric stress (i.e., the strength of the anisotropic part of the stress state), where:

[0105]

[0106] in, as well as represents the three principal stress components (i.e., principal stress components);

[0107]

[0108] in, is the deviatoric stress tensor component, describing the deviatoric stress remaining after removing the isotropic part of the stress state (the isotropic part is an amount of stress that is equal in all directions), and ,in, The total stress tensor is Component, describing the internal The stress components in the coordinate directions, Kronecker Symbol used to distinguish main diagonal elements from off-diagonal elements in tensor computations.

[0109] Therefore, in this embodiment, weather conditions are introduced into the Drucker-Prager model to dynamically adjust the yield criterion to reflect the stress state and failure characteristics of the rock mass in the actual environment, clarify the rupture or separation of the rock mass in the current mine, and facilitate subsequent block size analysis and prediction.

[0110] Step 2: Dynamically analyze the mechanical behavior of the mine blasting process using the finite element method to analyze the crack propagation of the rock mass, including:

[0111] S1. Establish a finite element model, then we have:

[0112] According to the actual mining situation, determine the geometric dimensions of the rock mass and blasting area, and perform geometric modeling (if the blasting area is a cuboid, the geometric model can be defined based on the length, width and height of the cuboid);

[0113] S2. Assign the updated rock mass strength parameters (friction angle and cohesion) to each material unit volume (friction angle and cohesion are applied to each unit of the rock mass. For other material properties (such as density, elastic modulus, Poisson's ratio, etc.), they should be assigned according to the characteristics of different rock layers and are not limited here);

[0114] S3. Divide the mine area into grids to ensure accurate simulation of the response of the rock mass during blasting. The steps of grid division include:

[0115] Select the mesh type, such as tetrahedral elements, hexahedral elements, or triangular / quadrilateral elements;

[0116] Grid density determines the size of the grid. Usually, key areas within the area (such as blasting areas) require finer grids.

[0117] The cell type, including cubic cells (Hexahedral) or tetrahedral cells;

[0118] It should be noted that meshing directly affects the accuracy and calculation time of finite element solution, and fine mesh helps to capture detailed changes in blasting.

[0119] S4. Setting boundary conditions and initial conditions. Under the influence of weather factors (such as rainfall and snowfall), the wetting effect and freeze-thaw effect of the mine rock mass will change its internal state. Therefore, in this embodiment, boundary conditions and initial conditions related to the temperature field and humidity field are set in the finite element model. Then,

[0120] Dynamic temperature field boundary conditions:

[0121] The freeze-thaw effect will cause crack expansion through the temperature field, that is, the dynamic boundary condition of the temperature field:

[0122] Temperature boundary conditions, freeze-thaw effects through temperature Changes in rock mass affect:

[0123]

[0124] in, represents the temperature at time t, represents the initial temperature, represents the temperature attenuation coefficient;

[0125] Temperature diffusion equation: The diffusion of temperature field in rock mass is expressed according to the heat conduction equation:

[0126]

[0127] in, Indicates the rock density, which affects the heat conduction rate. represents the specific heat capacity of rock mass, Expressing thermal conductivity, Represents the temperature field, describing the temperature distribution at each point in the rock mass. represents the partial derivative of temperature with respect to time, The Laplace operator representing temperature describes the rate of change of the temperature field in space and is used to quantify the diffusion or concentration trend of temperature, where:

[0128] Indicates the spatial coordinate direction.

[0129] Dynamic humidity field boundary conditions:

[0130] Wetting effect through pore pressure The change of affects the strength of rock mass, and the dynamic boundary conditions of humidity field include:

[0131] Humidity diffusion equation. The diffusion of humidity field is based on the diffusion equation:

[0132]

[0133] in, Indicates the water saturation of the rock mass, which indicates the volume ratio of the pores in the rock mass occupied by water. represents the rate of change of saturation over time, It represents the temperature diffusion coefficient, which describes the diffusion rate of water in the pores of the rock mass and is related to the pore characteristics, permeability and other parameters of the rock mass. represents the rate of change of saturation in space and quantifies the diffusion trend of humidity field, where: Indicates the spatial coordinate direction;

[0134] Humidity loading boundary, rainfall Convert to saturation:

[0135]

[0136] in, represents the initial saturation, It represents the conversion coefficient of rainfall to saturation, and describes the effect of unit rainfall on saturation.

[0137] Initial conditions, which are set as the rock mass state at the beginning of wetting and freeze-thaw, include:

[0138] Initial temperature field: set the initial temperature distribution of the rock mass (usually based on actual on-site measurement data, or determined by historical data, such as assuming that the initial temperature of the entire rock mass is constant);

[0139] Initial humidity field: Set the initial humidity distribution of the rock mass through the initial saturation set up.

[0140] S5. Solve the dynamic equation and analyze the dynamic response of the rock mass during mine blasting:

[0141] Including, establishing dynamic equations:

[0142]

[0143] in, represents the mass matrix, which is used to describe the mass distribution of the rock mass. represents the damping matrix, which is used to describe the energy dissipation, represents the stiffness matrix of the rock mass, describing the stiffness of the rock mass, represents the acceleration vector, which indicates the rate of change of velocity, represents the velocity vector, which indicates the rate of change of displacement, represents the displacement vector, which represents the displacement of each unit. Represents external load vectors, including blasting loads and dynamic loads introduced by weather effects, represents additional force;

[0144] Time stepping by explicit central difference method, discrete time step , iterative calculation of displacement ,speed and acceleration , including:

[0145] Time discretization, choosing the time step , discretize time into represents the discrete time point, then we have,

[0146] Displacement: ;

[0147] speed: ;

[0148] Acceleration: ;

[0149] in, as well as Represents discrete time displacement, velocity and acceleration at the time of

[0150] Acceleration:

[0151]

[0152] speed:

[0153]

[0154] in, and They represent the displacement of the next time step and the previous time step respectively, and are used in the recursive formula of the central difference method.

[0155] Discretization of dynamic equations:

[0156] Substituting the discretization of acceleration and velocity into the dynamic equation, we have:

[0157]

[0158] in, represents the discretized external load vector, See below for detailed explanation.

[0159] Therefore, after discretization, the recursive relationship is obtained:

[0160]

[0161] Arranging the recursive formula, we have,

[0162]

[0163] in, represents the left coefficient matrix, Indicates the external add-on on the right. represents the displacement contribution at the current moment, Represents the displacement contribution at the previous moment.

[0164] Solve the recursion formula:

[0165] To initialize, we have,

[0166] Initial displacement ;

[0167] Initial Speed ;

[0168] Initial acceleration

[0169] in, represents the initial external load vector.

[0170] Compute the initial time step:

[0171] Calculate the displacement of the first time step by the difference formula , then there is,

[0172]

[0173] Then perform iterative recursion, and for each time step n, calculate according to the recursive formula:

[0174]

[0175] Then, update the velocity and acceleration to get,

[0176] For speed :

[0177]

[0178] For acceleration :

[0179]

[0180] Furthermore, by simulating the blasting load, the external load vector in the dynamic equation is provided. (Simulate the propagation of stress waves during blasting to capture the dynamic response of the rock mass):

[0181] The blasting load is dynamically changing, so:

[0182]

[0183] in, represents the blast load at time t, describing the pressure wave that changes with time, Represents the initial blasting load, describing the maximum pressure at the beginning of blasting. represents the pressure wave attenuation coefficient, which describes the decay rate of the pressure wave over time, where:

[0184] After applying the blasting load, the external load vector is obtained , then:

[0185]

[0186] in, Indicates the area of ​​action;

[0187] To determine the actual external load vector .

[0188] Then the weather factors (humidification effect and freeze-thaw effect) are calculated through pore pressure and material property changes, including:

[0189] Wetting loading, pore pressure Influence of effective stress:

[0190]

[0191] in, It represents effective stress, describes the effective stress of rock mass under wetting, and represents the actual force borne by rock mass material. Represents the total stress in the rock mass, including pore pressure It should be noted that wetting loading reduces rock strength, so the pore pressure needs to be updated in real time.

[0192] Furthermore, in the finite element model, the rock mass is divided into a number of small units (each unit has a corresponding volume ), each unit has several nodes, and the pore pressure exerts additional force on the rock mass through these nodes, which is called additional force. It can be regarded as an additional external load acting on the unit node, similar to the load imposed by the external environment (such as earthquake, wind, etc.). Therefore, the additional force caused by pore pressure is Added to the external load vector On, forming the total external load, therefore, for , then there is,

[0193]

[0194] in, represents the volume of a finite element unit in the rock mass, represents the strain-displacement matrix, represents the transpose of the strain-displacement matrix, describing the inverse relationship from strain to displacement, Represents a unit volume element, which is used to represent a small increment of volume during numerical integration. Pore ​​pressure In volume Additional force inside.

[0195] It should be noted that wetting loading affects the pore pressure , changing the effective stress of the rock mass , and then modify the external load vector in the dynamic equation , to obtain the updated external load vector With additional force , which reflects the dynamic influence of wetting on the movement response of rock mass and facilitates the solution of the above dynamic equations.

[0196] Freeze-thaw loading (freeze-thaw loading and humidification loading are expressed as environmental loading), the temperature field changes the material properties, and the stiffness matrix is ​​calculated Dynamic updates, then there are,

[0197]

[0198] in, represents the stiffness matrix (it should be noted that the change of temperature field will directly affect the mechanical properties of the rock mass, causing the stiffness matrix to be dynamically adjusted over time and space, thereby affecting the overall motion response. Therefore, the updated stiffness matrix here is substituted into the above dynamic equation). represents the initial stiffness, represents the temperature sensitivity coefficient, Represents the temperature field. It should be noted that the stiffness matrix must be dynamically updated because the freeze-thaw effect weakens the rock stiffness. In addition, the wetting and freeze-thaw of the rock mass are dynamic processes and must be loaded step by step through time steps. The pore pressure and temperature affect the material properties, so the stiffness matrix and effective stress also need to be dynamically adjusted.

[0199] In the above embodiment, by defining the boundary constraints of the rock mass system, it is ensured that the dynamic equation has a unique solution, then,

[0200] Fixed boundaries (used to represent fixed constraints on the rock mass), Represents displacement, fixed boundary conditions set the displacement of certain areas to zero to ensure that the model does not displace on the boundary;

[0201] dynamic boundaries (representing changes in pore pressure due to rainfall or wetting), Represents the permeability coefficient of the rock mass.

[0202] Step 3: Further, with the influence of wetting effect and freeze-thaw effect, the failure criterion of rock mass needs to be adjusted (Mohr-Coulomb criterion, judging whether rock mass is destroyed based on the shear strength of rock mass) to reflect the change of its strength reduction and crack propagation behavior, including:

[0203] Under the effects of wetting and freeze-thaw, the friction angle and cohesion in the rock mass strength parameters in the Drucker-Prager model will change dynamically, and the crack extension criterion is:

[0204]

[0205] in, Represents shear stress, reflecting the driving force of slip inside the rock mass. It represents normal stress, which is the normal stress acting on the crack surface and reflects the compression or tension of the rock mass. represents the tangent of the friction angle, represents the friction angle, It indicates cohesion;

[0206] like , it means that the rock mass is damaged and the cracks begin to expand. It represents shear strength and describes the maximum shear stress that the rock mass can withstand when it is destroyed.

[0207] In the above, it should be noted that the crack extension criterion is used to determine whether the rock mass is damaged, and the damaged rock mass forms cracks, which divide the rock mass into different blocks. Since the size of the block is determined by the geometric shape and distribution of the cracks, in this embodiment, the block size can be defined based on the geometric shape of the cracks. , using the Rosin-Rammler distribution description, we have,

[0208]

[0209] in, Indicates that the particle size is smaller than The block ratio of It indicates the characteristic particle size, which is the scale parameter of block size distribution. The larger the characteristic particle size, the larger the overall size of the block. Represents the distribution index, describing the concentration of block distribution. It means that the particle size distribution is narrower and the block size is more concentrated. Therefore, based on the above crack distribution in the rock mass, the minimum size of each block can be calculated. , and in this embodiment, the friction angle is adjusted by introducing the weather conditions, namely the humidification and freeze-thaw effects mentioned above. and cohesion , in order to change the crack extension criterion, it is beneficial to analyze and calculate the distribution of rock cracks and the size of blocks mentioned above, thereby providing auxiliary evaluation and judgment basis and decision-making for the effect of mine blasting.

[0210] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing and predicting the fragmentation of ore blasting, characterized in that: The steps include: The weather state is introduced into the Drucker-Prager model to clarify the friction angle and cohesion affected by the wetting effect and freeze-thaw effect in the weather state; According to the friction angle and cohesion, the friction angle correction parameter and cohesion correction parameter in the Drucker-Prager model are determined and substituted into the yield function to determine whether the rock mass has yielded and whether the current rock mass is broken or separated. The dynamic equation is established by the finite element method to clarify the dynamic response of the rock mass under blasting load and environmental load, where: The expression of the dynamic equation is: in, represents the mass matrix, represents the damping matrix, represents the stiffness matrix of the rock mass, represents the acceleration vector, represents the velocity vector, represents the displacement vector, represents the external load vector, represents additional force; Based on the crack extension criterion, it is judged whether the rock mass is damaged and cracks are generated under stress, and the blasting block size is predicted based on the rock mass cracks.

2. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The friction angle and cohesion affected by the wetting effect and the freeze-thaw effect are determined according to the following relationship: in, and They represent the friction angle and cohesion of the rock mass after being affected by the wetting effect and the freeze-thaw effect, respectively. represent the initial friction angle and cohesion respectively, and They represent the attenuation sensitivity coefficients of crack density to friction angle and cohesion respectively, represents the density of joints and cracks, and are the attenuation sensitivity coefficients of pore pressure to friction angle and cohesion, respectively. Represents the pore pressure.

3. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 2, characterized in that: The method for judging whether the rock mass yields is: The parameters of the Drucker-Prager model are determined based on the friction angle and cohesion under the wetting effect and freeze-thaw effect, and then: in, represents the friction angle correction parameter in the Drucker-Prager model, represents the cohesion correction parameter in the Drucker-Prager model; Introducing the friction angle correction parameter and the cohesion correction parameter into the Drucker-Prager yield function, it is determined whether the rock mass yields under a given stress state, and then: in, represents the value of the Drucker-Prager yield function, represents the stress tensor, represents the first invariant under the stress tensor, represents the second invariant of the deviatoric stress tensor; Among them, if When it is 0, the rock mass is judged to be in a yield state.

4. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 3, characterized in that: The second invariant The solution is: in, is the deviatoric stress tensor Quantity; in, The total stress tensor is Quantity, Kronecker symbol.

5. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The steps to establish dynamic equations by finite element method to clarify the dynamic response of rock mass under blasting load and environmental load are as follows: Establish a finite element model, determine the geometric dimensions of the rock mass and blasting area according to the actual mining conditions, and perform geometric modeling; assigning updated rock mass strength parameters to each material unit volume; Divide the mine area into grids. The steps of grid division include: Select the mesh type, including tetrahedral elements, hexahedral elements, triangular elements, or quadrilateral elements; Set the mesh density; Set boundary conditions and initial conditions, including: Dynamic temperature field boundary conditions, freeze-thaw effect through temperature If the change of affects the rock mass, then we have in, represents the temperature at time t, represents the initial temperature, represents the temperature attenuation coefficient; Dynamic humidity field boundary conditions, humidification effect through pore pressure If the change of affects the rock mass strength, then we have: The diffusion of humidity field is based on the diffusion equation: in, represents the water saturation of the rock mass, represents the rate of change of saturation over time, represents the temperature diffusion coefficient, Indicates the rate of change of saturation in space; Humidity loading boundary, rainfall Convert to saturation: in, represents the initial saturation, It represents the conversion coefficient of rainfall to saturation, describing the effect of unit rainfall on saturation; Initial conditions, set to the rock state at the beginning of wetting and freeze-thaw, include: Initial temperature field: preset the initial temperature distribution of the rock mass; Initial humidity field: through the initial saturation set up; The dynamic equations are formulated and solved by the central difference method.

6. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The external load vector The method to determine is: The blasting load changes dynamically, then: in, represents the blasting load at time t, represents the initial blasting load, represents the pressure wave attenuation coefficient, where: The external load vector is obtained after applying the blasting load , then: in, Indicates the area of ​​action.

7. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 2, characterized in that: The additional force According to the following relationship: in, represents the volume of a finite element unit in the rock mass, represents the strain-displacement matrix, represents the transpose of the strain-displacement matrix, Represents a unit volume element.

8. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The stiffness matrix The solution is: in, represents the stiffness matrix, represents the initial stiffness, represents the temperature sensitivity coefficient, Represents the temperature field.

9. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The crack extension criterion for judging whether the rock mass is damaged and cracks are generated under stress is as follows: in, represents the shear stress, represents the normal stress, represents the tangent of the friction angle, represents the friction angle, It indicates cohesion; like , it means that the rock mass is damaged and the cracks begin to expand. Indicates shear strength.

10. The method for analyzing and predicting the blasting fragmentation of an ore according to claim 1, characterized in that: The method for predicting blasting size is: Define fragmentation based on fracture geometry ; Using the Rosin-Rammler distribution description, we have, in, Indicates that the particle size is smaller than The block ratio of , It represents the characteristic particle size and the scale parameter of the block size distribution. Represents the distribution index.

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