CN115565625A - Long-term mechanical property model characterization method for diversified industrial solid waste filling material - Google Patents

Long-term mechanical property model characterization method for diversified industrial solid waste filling material Download PDF

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CN115565625A
CN115565625A CN202210696731.9A CN202210696731A CN115565625A CN 115565625 A CN115565625 A CN 115565625A CN 202210696731 A CN202210696731 A CN 202210696731A CN 115565625 A CN115565625 A CN 115565625A
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王烁康
闫晶晶
范志东
杨瑞臣
耿小丕
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Chengde Petroleum College
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Abstract

The invention discloses a long-term mechanical property model characterization method for a diversified industrial solid waste filling material, and relates to the technical field of coal mining; the method comprises the steps of sequentially establishing a filling material creep constitutive model, a filling block bearing mechanical model and a filling stope mutation mathematical model, and quantifying the model of the filling material in the whole process from development to bearing to realize quantitative representation of the long-term mechanical property of the filling material; the method can solve the limitation of small application range of the existing empirical formula, provides basis for comprehensive utilization of industrial solid wastes and control of mining and charging time, and can be applied to the field of green mining of coal mines such as' three-coal-seam safety mining, aquifer in-situ protection mining, industrial solid waste filling mining, development of roadway protection coal pillar recovery and the like.

Description

Long-term mechanical property model characterization method for diversified industrial solid waste filling material
Technical Field
The invention relates to the technical field of coal mining, in particular to a long-term mechanical property model characterization method for a diversified industrial solid waste filling material.
Background
At present, in the field of coal mining, some scholars research the blending utilization aspect of gangue, fly ash, sandy soil and municipal solid waste, develop paste filling materials and cemented filling materials, and analyze the influence rule of external factors such as temperature, acid corrosion and the like on the mechanical strength of a filling body. However, the evaluation of the bearing stability of the filling material and other aspects are mainly based on an empirical formula, and particularly, the related technical level and the research method are not perfect aiming at the research of the long-term mechanical property of the industrial solid waste filling material.
Disclosure of Invention
Aiming at the technical defects, the invention aims to provide a long-term mechanical property model characterization method for a diversified industrial solid waste filling material, which can quantify the model of the filling material in the whole process from development to bearing, realize long-term mechanical property characterization and provide a basis for comprehensive utilization of industrial solid waste and control of the sampling and filling time.
In order to solve the technical problem, the invention adopts the following technical scheme:
the invention provides a long-term mechanical property model characterization method for a diversified industrial solid waste filling material, which comprises the following steps of:
(1) Pouring the prepared diversified industrial solid waste filling slurry into a mold, and preparing cylindrical filling material samples with the ages of 3 days, 7 days and 28 days respectively and the specification of phi 50mm multiplied by 100 mm; acquiring a conventional triaxial stress-strain curve and a graded creep curve of a sample by using rock mechanical property testing equipment;
(2) Setting a rheological element capable of describing an accelerated creep stage of the filling material by taking the test result in the step (1) as a main basis, constructing a creep constitutive model capable of representing the whole process of instantaneous deformation, deceleration creep, constant-speed creep and accelerated creep of the filling material, and identifying model parameters;
(3) The method includes the steps that (1) the coal seam top floor is studied to study the clamping mechanical action mechanism of the coal seam top floor on a filling body in combination with the mine pressure display characteristics of a working face, the boundary condition of compression deformation of the filling body is analyzed, a filling body bearing mechanical model is constructed, and the bearing compression characteristics of the filling body are explained;
(4) Based on the research on the energy conversion characteristics of overlying strata and filling bodies in the compression deformation process of the filling bodies, a mutation mathematical model of the damage instability of the filling bodies is established by combining a mutation theory, the critical deformation of the damage instability of the filling bodies is given, and the judgment standard of the stable bearing of the filling bodies is obtained;
(5) And (4) integrating the three models in the steps (2) to (4) to form a long-term mechanical property characterization model of the diversified industrial solid waste filling material, sequentially providing mechanical properties of the filling body by using the constitutive model, providing boundary conditions of the filling body by using the mechanical model, and judging the bearing effect of the filling body by using the mathematical model.
Preferably, in the step (2), the setting of the filling material accelerated creep element needs to consider the influence of the initial damage effect, and set the setting as a nonlinear plastic damaged element, i.e. NPDM, the plastic damaged unit of the NPDM is composed of a damaged part and an undamaged part, wherein the damaged part is composed of the initial damage and the creep damage, and the creep equation of the NPDM considering the initial damage effect is as follows:
Figure BDA0003702456540000021
in the formula, E N NPDM elastic modulus, GPa; sigma s Yield stress, mpa; sigma ds Is an offset stress, i.e. sigma ds =σ 13 ,Mpa;D 0 Initial damage before creep; r is a constant determined by the fill material properties.
Preferably, when the creep constitutive model is constructed in the step (2), a Hook body, a Kelvin body, a Bingham body and an NPDM (non-linear numerical control) body are connected in series, and a Newton body contained in the rheological element is replaced by an Abel clay pot, so as to establish the filling material nonlinear fractional order creep constitutive model, wherein a creep equation of the creep constitutive model is as follows:
Figure BDA0003702456540000031
in the formula, σ sB Starting a stress threshold value of the Bingham body, namely MPa; sigma sN Starting a stress threshold value, MPa, for NPDM; k is H Volume modulus for Hook volume, GPa; g H Hook body shear modulus, GPa; g K Kelvin bulk shear modulus, GPa; eta K Is viscosity coefficient, MPa.s; alpha and omega are derivative orders, alpha is more than or equal to 0 and less than or equal to 1, omega is more than or equal to 0 and less than or equal to 1; e α,α+1 Is a Mittag-Leffler function with the variable alpha, considered as a constant in this model; Γ (1 + ω) is a function of Γ, with its variable ω, considered to be constant in the model.
Preferably, in the step (2), when identifying the model parameters, the model parameters are divided into three types, namely, test solution parameters, equation solution parameters and fitting solution parameters, and a classification solution method is adopted to identify the model parameters, specifically:
(1) The test solution parameter is a starting stress threshold value sigma sB And σ sN Respectively corresponding to the minimum stress values of volume expansion and volume expansion in the creep test of the filling material test piece in the step (1);
(2) The equation solution parameter is instantaneous deformation parameter K H And G H Solving a simultaneous equation set at the moment of t =0 by using a creep equation of the filling material nonlinear fractional order creep constitutive model;
(3) The fitting solution parameters refer to parameters which can not be solved by simultaneous equations and need to be determined by a numerical fitting method, and comprise G K 、α、η K 、E α,α+1 、ω、η B 、Γ(1+ω)、K N 、G N And r, solving the nonlinear least square problem by adopting an LM algorithm.
Preferably, in step (3), the following basic assumptions are made in constructing the filling body bearing mechanical model: (1) The technology can effectively control the roof, and the relative mining height of the subsidence of the roof is a minimum; (2) the filling body meets the basic condition of ideal elastoplastomer; (3) The deformation characteristic of the filling body can be simplified into the plane strain problem; (4) the overlying strata apply uniform load action to the filling body; based on the basic assumptions, the calculation formula of the compression deformation of the filling body is as follows:
Figure BDA0003702456540000041
in the formula, M is the mining height M; q is overburden load, mpa; e 1 Is the elastic modulus of the coal body, GPa; e 2 The elastic modulus of the filling body is GPa; lambda [ alpha ] 1 The regression stress coefficient obtained in the second step is Mpa; lambda [ alpha ] 2 The regression adjustment coefficient obtained in the step two is obtained; n is the number of filling mining stages, and when the working face is not divided into mining stages, N =1; n is the number of mining stages, and when the face does not divide a mining stage, n =1.
Preferably, in the step (4), the constructing of the abrupt mathematical model of the filler destabilization includes four steps, specifically: (1) Selecting a mutation model according to the dimension of the control variable and the state variable of the research problem; (2) Establishing an energy balance equation of interaction of the overburden and the filling body, and expanding the energy balance equation by using a Taylor formula; (3) Reserving the same order in the expansion equation as the equilibrium surface equation of the mutation model, and arranging the order into a standard form; (4) And determining a standard-form parameter and a divergence point set, and judging whether the overburden rock and the filling body have energy mutation or not by using a mutation theory.
The invention has the beneficial effects that:
the method carries out model quantization on the filling material in the whole process from development to bearing, and provides mechanical properties, obtains boundary conditions and explains the bearing effect for the representation of the long-term mechanical property of the filling material by sequentially establishing a filling material creep constitutive model, a filling block bearing mechanical model and a filling stope mutation mathematical model. The method has the advantages of rigorous logic, clear layers and convenient calculation, can solve the limitation of small application range of the existing empirical formula, and can provide a basis for the comprehensive utilization of industrial solid wastes and the control of the mining and charging time, thereby improving the social, economic and environmental benefits of coal mining.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a 28-day age graded creep curve for a fill material according to an example of the present invention.
FIG. 2 is a filling material nonlinear fractional order creep constitutive model according to an embodiment of the present invention.
Fig. 3 is a model of the pressure of the filling body and a model of the loading mechanics thereof according to an embodiment of the invention.
FIG. 4 is a mathematical model of the filling body destabilization by cusp mutation according to the embodiment of the invention.
FIG. 5 is a flow chart of long-term mechanical property model characterization of the diversified industrial solid waste filling material of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1 to fig. 5, in this embodiment, a long-term mechanical property model characterization method of a diversified industrial solid waste filling material is elaborated by taking a certain continuous mining and continuous filling working face as an example. The working face of the embodiment adopts a roadway mining and filling mode to recover coal resources. The average burial depth of the working face is about 390m, the average thickness of the mined coal seam is about 2.5m, and the coal seam is a nearly horizontal coal seam. The embodiment provides a method for representing long-term mechanical property models of diversified industrial solid waste filling materials, which comprises the following steps of:
firstly, selecting fly ash as filling aggregate, and preparing industrial solid waste filling material slurry by matching with additives known by persons skilled in the art, such as cement, an early strength agent, a water reducing agent, a retarder, a coagulant, a synergist and the like, wherein the mixing amount of the fly ash is more than or equal to 70%, other mixing ratios adopt mixing ratios known by persons skilled in the art, and the specific preparation method of the industrial solid waste filling material slurry adopts the existing preparation method known by persons skilled in the art, and is not specifically described; preparing 10 cylindrical filling material samples with the ages of 3 days, 7 days and 28 days respectively, and the specification of phi 50mm multiplied by 100 mm; by using rock mechanical property testing equipment, the conventional triaxial stress strain characteristics of the filling material test piece of 3-day, 7-day and 28-day ages are tested by using a GDS triaxial test system, and the graded creep stress grade is determined according to the conventional triaxial stress strain characteristics, so that the graded creep characteristic of the test piece of 28-day ages is obtained, which is shown in figure 1;
step two, setting a nonlinear plastic damage element (NPDM) which is used for describing the accelerated creep stage of the filling material by taking the test result in the step one as the main basis and considering the influence of the initial damage effect; the plastic damage unit of the NPDM consists of a damaged part and an undamaged part, wherein the damaged part consists of initial damage and creep damage; the creep equation is:
Figure BDA0003702456540000061
in the formula, E N NPDM elastic modulus, GPa; sigma s Yield stress, mpa; sigma ds Is an offset stress, i.e. sigma ds =σ 13 ,Mpa;D 0 Initial damage before creep; r is a constant determined by the filling material properties;
secondly, a Hook body, a Kelvin body, a Bingham body and an NPDM are connected in series, a Newton body contained in the NPDM is replaced by an Abel clay pot, a filling material nonlinear fractional order creep constitutive model capable of representing the whole process of instantaneous deformation, deceleration creep, constant creep and acceleration creep of the filling material is established, and a creep equation of the model is as follows:
Figure BDA0003702456540000062
in the formula, σ sB Starting a stress threshold value of the Bingham body, namely MPa; sigma sN Starting a stress threshold value, MPa, for NPDM; k H Hook bulk modulus, GPa; g H Hook body shear modulus, GPa; g K Kelvin bulk shear modulus, GPa; eta K Is viscosity coefficient, MPa.s; both alpha and omega are derivative orders, alpha is more than or equal to 0 and less than or equal to 1, and omega is more than or equal to 0 and less than or equal to 1; e α,α+1 Is a Mittag-Leffler function with the variable alpha, considered as a constant in this model; Γ (1 + ω) is a Γ function, the variable of which is ω, considered constant in the model;
then, dividing the model parameters in the formula (2) into three types, namely test solving parameters, equation solving parameters and fitting solving parameters, and identifying the model parameters by adopting a classification solving method, which specifically comprises the following steps:
(1) The test solution parameter is a starting stress threshold value sigma sB And σ sN Respectively corresponding to the minimum stress values of volume expansion and volume expansion in the creep test of the filling material test piece in the step one;
(2) The equation solution parameter is instantaneous deformation parameter K H And G H Using a formula (2), solving a simultaneous equation set at the time when t = 0;
(3) The fitting solution parameters refer to parameters which can not be solved by simultaneous equations and need to be determined by a numerical fitting method, and comprise G K 、α、η K 、E α,α+1 、ω、η B 、Γ(1+ω)、K N 、G N And r, solving the nonlinear least square problem by adopting an LM algorithm (Levenberg-Marquarelt algorithm);
finally, the creep equation expression of the filling material in the embodiment is obtained as follows:
Figure BDA0003702456540000071
step three, in combination with the mine pressure display characteristics of the working face, researching the clamping mechanical action mechanism of the coal seam roof and floor to the filling body, analyzing the boundary conditions of the compression deformation of the filling body, and making the following basic assumptions: (1) The technology can effectively control the top plate, and the subsidence of the top plate is extremely small relative to the mining height; (2) the filling body meets the basic condition of ideal elastoplastomer; (3) The deformation characteristic of the filling body can be simplified into a plane strain problem; (4) the overlying strata apply uniform load action to the filling body; on the basis, a filling body bearing mechanical model is constructed, and the bearing compression characteristic of the filling body is explained, which is shown in figure 3; from this, the calculation formula of the compression deformation of the filling body is as follows:
Figure BDA0003702456540000072
in the formula, M is the mining height M; q is overburden load, mpa; e 1 Is the elastic modulus of the coal body, GPa; e 2 Is the elastic modulus of the filling body, GPa; lambda [ alpha ] 1 The regression stress coefficient obtained in the second step is Mpa; lambda [ alpha ] 2 The regression adjustment coefficient obtained in the step two is obtained; n is the number of filling mining stages, and when the working face is not divided into mining stages, N =1; n is an ordinal number of an exploitation stage, and when the working face does not divide the exploitation stage, n =1;
step four, based on the research on the energy conversion characteristics of overlying strata and filling bodies in the compression deformation process of the filling bodies, combining the mutation theory, and constructing a mutation mathematical model of the filling body damage instability by adopting the following steps:
(1) In the examples, the control variable of the problem studied was 2-dimensional and the state variable was 1-dimensional, and therefore, the cusp mutation model was selected, see fig. 4;
(2) Establishing an energy balance equation of interaction of the overburden and the filling body, and expanding the energy balance equation by using a Taylor formula;
(3) The same order in the expansion equation as the equilibrium surface equation of the mutation model is reserved, and the third derivative is reserved in the embodiment and is arranged into a standard form;
(4) Determining standard parameters and branch point set, and determining whether the overburden rock and the filling body have energy mutation by using mutation theory, wherein in the embodiment, the discriminant of the filling body having mutation instability can be sorted into
Figure BDA0003702456540000081
When Δ > 0, the filling body is considered to be kept in a stable state; when Δ =0, the filler is considered to be in a destabilization critical state; when Δ < 0, the pack is considered to be in an unstable state;
step five, combining the three models in the step two to the step four into a whole to form a long-term mechanical property representation model of the diversified industrial solid waste filling material, sequentially providing mechanical properties of the filling body by using the constitutive model, providing boundary conditions of the filling body by using the mechanical model, and judging the bearing effect of the filling body by using the mathematical model; then determining whether industrial solid waste filling exploitation can be carried out according to judgment, wherein the main flow is shown in figure 5; the result shows that when continuous mining and continuous filling mining is adopted, four mining stages are divided, and in order to ensure that a filling body does not generate mutation and instability, the waiting time range after stope branch roadway filling is controlled to be 37-131 days; after the stope branch roadway is filled, at least 37 days are required to wait for the next mining adjacent coal pillar, and after the filling body is loaded, sufficient-strength lateral constraint needs to be provided for the filling body within 131 days.
The method for representing the long-term mechanical property model of the diversified industrial solid waste filling material can be applied to the fields of coal mine green mining, such as' three-coal-seam safety mining, aquifer in-situ protection mining, industrial solid waste filling mining, development roadway protection coal pillar recovery and the like.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (6)

1. The method for representing the long-term mechanical property model of the diversified industrial solid waste filling material is characterized by comprising the following steps of:
(1) Pouring the prepared diversified industrial solid waste filling slurry into a mold, and preparing cylindrical filling material samples with the ages of 3 days, 7 days and 28 days respectively and the specification of phi 50mm multiplied by 100 mm; acquiring a conventional triaxial stress-strain curve and a graded creep curve of a sample by using rock mechanical property testing equipment;
(2) Setting a rheological element capable of describing an accelerated creep stage of the filling material by taking the test result in the step (1) as a main basis, constructing a creep constitutive model capable of representing the whole process of instantaneous deformation, deceleration creep, constant-speed creep and accelerated creep of the filling material, and identifying model parameters;
(3) The method is characterized by comprising the following steps of (1) researching a clamping mechanical action mechanism of a coal seam top floor to a filling body by combining the mine pressure display characteristics of a working face, analyzing boundary conditions of compression deformation of the filling body, constructing a filling body bearing mechanical model, and explaining the bearing compression characteristics of the filling body;
(4) Based on the research on the energy conversion characteristics of overlying strata and filling bodies in the compression deformation process of the filling bodies, a mutation mathematical model of the damage instability of the filling bodies is established by combining a mutation theory, the critical deformation of the damage instability of the filling bodies is given, and the judgment standard of the stable bearing of the filling bodies is obtained;
(5) And (4) integrating the three models in the steps (2) to (4) to form a long-term mechanical property characterization model of the diversified industrial solid waste filling material, sequentially providing mechanical properties of the filling body by using the constitutive model, providing boundary conditions of the filling body by using the mechanical model, and judging the bearing effect of the filling body by using the mathematical model.
2. The method for characterizing the long-term mechanical property model of the diversified industrial solid waste filling material according to claim 1, wherein in the step (2), the setting of the filling material accelerated creep element needs to consider the influence of an initial damage effect, and the setting is a nonlinear plastic damage element (NPDM), wherein a plastic damage unit of the NPDM consists of a damaged part and an undamaged part, the damaged part consists of initial damage and creep damage, and an NPDM creep equation considering the initial damage effect is as follows:
Figure FDA0003702456530000011
in the formula, E N Is NPDM elastic modulus, GPa;σ s Yield stress, mpa; sigma ds Is an offset stress, i.e. sigma ds =σ 13 ,Mpa;D 0 Initial damage before creep; r is a constant determined by the fill material properties.
3. The method for characterizing the long-term mechanical property model of the diversified industrial solid waste filling material according to claim 1, wherein when the creep constitutive model is constructed in the step (2), a Hook body, a Kelvin body, a Bingham body and an NPDM (non-positive pressure differential) body are connected in series, and a Newton body contained in the rheological element is replaced by an Abel clay pot, so that the nonlinear fractional order creep constitutive model of the filling material is established, wherein a creep equation of the model is as follows:
Figure FDA0003702456530000021
in the formula, σ sB Starting a stress threshold value, MPa, for the Bingham body; sigma sN Starting a stress threshold value, MPa, for NPDM; k H Volume modulus for Hook volume, GPa; g H Is Hook body shear modulus, GPa; g K Kelvin bulk shear modulus, GPa; eta K Is viscosity coefficient, MPa · s; alpha and omega are derivative orders, alpha is more than or equal to 0 and less than or equal to 1, omega is more than or equal to 0 and less than or equal to 1; e α,α+1 Is Mittag-Leffler function, the variable of which is alpha and is regarded as constant in the model; Γ (1 + ω) is a function of Γ, with its variables ω, considered constant in the model.
4. The method for characterizing the long-term mechanical property model of the diversified industrial solid waste filling material according to claim 3, wherein in the step (2), when model parameter identification is performed, the model parameters are divided into three types, namely test solution parameters, equation solution parameters and fitting solution parameters, and a classification solution method is adopted to perform the model parameter identification, specifically:
(1) The test solution parameter is a starting stress threshold value sigma sB And σ sN Respectively corresponding to the occurrence of volume expansion and volume expansion in the creep test of the filling material test piece in the step (1)A minimum stress value of the container;
(2) The equation solution parameter is instantaneous deformation parameter K H And G H Solving a simultaneous equation set at the moment of t =0 by using a creep equation of the filling material nonlinear fractional order creep constitutive model;
(3) The fitting solution parameters refer to parameters which can not be solved by simultaneous equations and need to be determined by a numerical fitting method, and comprise G K 、α、η K 、E α,α+1 、ω、η B 、Γ(1+ω)、K N 、G N And r, solving the nonlinear least square problem by adopting an LM algorithm.
5. The method for characterizing the long-term mechanical property model of the diversified industrial solid waste filling material according to claim 1, wherein in the step (3), the following basic assumptions are made in constructing the filling body bearing mechanical model: (1) The technology can effectively control the top plate, and the subsidence of the top plate is extremely small relative to the mining height; (2) the filling body meets the basic condition of ideal elastoplastomer; (3) The deformation characteristic of the filling body can be simplified into a plane strain problem; (4) the overlying strata exert uniform load action on the filling body; based on the basic assumption, the calculation formula of the compression deformation of the filling body is as follows:
Figure FDA0003702456530000031
in the formula, M is the mining height M; q is overburden load, mpa; e 1 Is the elastic modulus of the coal body, GPa; e 2 The elastic modulus of the filling body is GPa; lambda [ alpha ] 1 The regression stress coefficient obtained in the second step is Mpa; lambda [ alpha ] 2 The regression adjustment coefficient obtained in the second step; n is the number of filling mining stages, and when the working face is not divided into mining stages, N =1; n is the number of mining phases, and when the working face does not divide a mining phase, n =1.
6. The method for characterizing the long-term mechanical property model of the diversified industrial solid waste filling material according to claim 1, wherein in the step (4), the step of constructing the abrupt change mathematical model of the filling body damage instability comprises four steps, specifically: (1) Selecting a mutation model according to the dimension of the control variable and the state variable of the research problem; (2) Establishing an energy balance equation of interaction of the overburden and the filling body, and expanding the energy balance equation by using a Taylor formula; (3) Reserving the order of the expansion equation which is the same as the order of the equilibrium curved surface equation of the mutation model, and sorting the order into a standard form; (4) And determining parameters and a divergence point set in a standard form, and judging whether the overburden rock and the filling body have energy mutation by using a mutation theory.
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