CN114062512B - Damage analysis method for fiber reinforced superfine tailing cementing material - Google Patents
Damage analysis method for fiber reinforced superfine tailing cementing material Download PDFInfo
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- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 1
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Abstract
A damage analysis method of fiber reinforced superfine tailing cementing materials comprises the steps of manufacturing test pieces of different fiber superfine reinforced tailing cementing materials, carrying out acoustic emission test on the test pieces under the condition of uniaxial compression, analyzing damage evolution of the test pieces under the action of load from 3 aspects of acoustic emission energy, ringing count and acoustic emission amplitude fractal dimension, and establishing a coupling relation of acoustic emission cumulative ringing count and strain by taking time as an intermediate quantity for calculation and analysis. According to the method, acoustic emission tests under the uniaxial compression condition are carried out by selecting different fiber reinforced ultrafine tailing cementing material test pieces, the time is taken as an intermediate quantity, and the coupling relation between the acoustic emission cumulative ringing count and the stress and damage variables is established.
Description
Technical Field
The invention belongs to the technical field of metal ore filling exploitation, and particularly relates to a damage analysis method of a fiber reinforced superfine tailing cementing material.
Background
In backfill mining, the mechanical properties of the cemented filling body (CPB) directly determine the safety of underground deep mining operations. In recent years, a great number of students at home and abroad develop a great deal of researches on mechanical properties of the filling body, unconfined uniaxial compression and splitting tensile strength tests are carried out on filling bodies with different proportions, a filling body pulling and compression state damage evolution equation and a damage constitutive model established by test data can better describe damage evolution properties and damage processes of the filling body, meanwhile, a great number of students introduce acoustic emission and other methods to develop further researches on mechanical properties of the filling body in the damage process, and the students also carry out uniaxial compression and Brazilian splitting tests on the tantalum-niobium tailing cemented filling body, and utilize the damage model and the energy fractal dimension based on acoustic emission ringing count rate to research the relations between damage variables and fractal dimension in the deformation damage process of the filling body, acoustic emission parameters and mechanical damage mechanism. In the aspect of fiber reinforced materials, more researches are carried out on concrete house construction, roads and bridges and the like in China, but the researches on the mine waste tailing fiber reinforced superfine tailing cementing materials and the analysis on the damage evolution rules and acoustic emission characteristics in deformation damage of different fiber reinforced superfine tailing cementing materials are less; because the geographical conditions of mines are complex and various, the method for researching models and damage analysis of houses and the like cannot be applied to mines as such, and fiber reinforced ultrafine tailing cementing materials and the like belong to ductile damage materials, mine production safety risks such as unstable stope ground pressure, deep well rock burst, surface subsidence, easy subsidence of goafs and the like can be possibly caused by the fact that the materials are not predicted in advance.
Disclosure of Invention
The invention aims to provide a method for establishing the coupling relation between acoustic emission cumulative ringing count and stress and damage variable by researching mechanical properties and acoustic emission properties in the compression process of different fiber reinforced superfine tailing cementing materials, so that the damage mechanism, compressive strength and damage evolution of the fiber reinforced superfine tailing cementing materials can be rapidly and accurately predicted, and scientific reference basis is provided for guaranteeing mine production safety and engineering of related industries.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a damage analysis method of fiber reinforced superfine tailing cementing material comprises the following steps:
step one, manufacturing test pieces of different fiber reinforced superfine tailing cementing materials;
step two, respectively carrying out acoustic emission tests on each test piece under the condition of uniaxial compression;
analyzing the damage evolution of the test piece under the load action from three aspects of acoustic emission energy, ringing count and acoustic emission amplitude fractal dimension;
and step four, establishing a coupling relation between the acoustic emission ringing cumulative count and the strain by taking time as an intermediate quantity for calculation and analysis, wherein the calculation and analysis process is as follows:
the strain control and the sound emission synchronous monitoring of the loading system are adopted, and the relationship between the strain and the time in the loading process is as follows:
ε＝kt+ε 0
(1)
wherein epsilon is the strain of the superfine tailing cementing material and has no dimension; k is a coefficient, and is obtained through the relation between fitting time and strain; t is the time in the loading process, and the unit is s; epsilon 0 The initial strain of the fiber reinforced superfine tailing cementing material can be obtained by linear fitting according to test data;
the relation between the cumulative ringing count N of the acoustic emission and the time t is combined and is represented by an S-shaped growth function, namely:
wherein A1, A2, B1 and B2 are constants, and can be directly obtained from the relation between fitting time and acoustic emission cumulative ringing count;
fitting the test result by using the formula (2), and combining the formula (1) and the formula (2) to obtain the coupling relation between the acoustic emission cumulative ringing count and the strain of the fiber reinforced superfine tailing cementing material:
the damage constitutive model of the fiber reinforced superfine tailing cementing material is expressed as follows:
σ＝Eε(1-D) (4)
wherein: sigma is effective stress in MPa; e is the deformation modulus of the material, and the unit is MPa; epsilon is the strain; d is a damage variable;
the strength of the fiber reinforced superfine tailing cementing material is subjected to Weibull random distribution, and the probability density expression is as follows:
wherein: m and F0 are Weibull random distribution parameters, wherein m is a shape parameter, and F0 is a proportion parameter; f is the fiber reinforced ultra fine tailings cementing material infinitesimal strength distribution variable (either stress or strain, here strain);
definition under the condition of displacement control and loading, the damage variable D of the micro-unit of the superfine tailing cementing material is N number of damaged micro-units b Ratio to total number of mesoscopic units N:
in the interval [0,F ], the number of the microscopic units for failure of the fiber reinforced superfine tailing cementing material is any interval,
substituting the formula (7) into the formula (6) to obtain the damage variable of the fiber reinforced superfine tailing cementing material under the condition of system strain control loading:
from formula (8), the introduced mesoscopic unit strength cannot directly characterize the damage variable of the fiber reinforced ultra-fine tailing cementing material, assuming that the mesoscopic unit of the fiber reinforced ultra-fine tailing cementing material meets the maximum tensile strain yield failure criterion, i.e.
F＝f(ε)＝ε f (9)
Epsilon in f Peak strain for the fine units of fiber reinforced ultra fine tailings cementing material;
substituting the formula (9) into the formula (8) to be connected in parallel with the vertical (4), and pushing out the constitutive model of the stress-strain curve of the fiber reinforced superfine tailing cementing material as follows:
order theSimultaneous equation set resolution of m and F 0 ：
Wherein: sigma (sigma) f Peak stress in MPa; epsilon f Peak strain of a microscopic unit of the fiber reinforced superfine tailing cementing material, and alpha is the effective damage rate;
the coupling relation between the acoustic emission accumulated ringing count N of the fiber reinforced ultra-fine tailing cementing material and the stress sigma and damage variable D under the uniaxial compression condition can be obtained by the coupling type (2) and the formula (10):
and calculating stress and damage variables of the fiber-reinforced superfine tailing cementing material through acoustic emission cumulative ringing count, wherein when the damage variables are close to 1, the fiber-reinforced superfine tailing cementing material tends to be in a complete damage state.
Further, the fiber reinforced superfine tailing cementing material test piece in the first step adopts cementing materials with the mass concentration of 65% and the sand-lime ratio of 1:6 of tailing to cement, and is respectively doped with three fiber reinforced superfine tailing cementing materials of glass fiber, polyacrylonitrile fiber and glass and polyacrylonitrile mixed fiber.
Further, in the loading strain test adopted in the acoustic emission test in the second step, the loading speed is 0.5mm/min, the loading is stopped when the test piece is damaged, the sampling threshold value of acoustic emission and the gain value of the preamplifier are both 40dB, and the sensor frequency is 20-100 kHz.
Further, the lesion evolution in step three includes: the mechanical property analysis is that the size of a strain value when a test piece is damaged is used for defining the damage mode as ductile damage; the acoustic emission characteristic analysis is to respectively draw stress-energy-time and stress-ringing count-time relation diagrams of different fiber ultrafine tailing cementing materials through received acoustic emission signal parameters, and divide the destruction process into three stages of an ascending period, a calm period and an active period; and the acoustic emission fractal dimension analysis is to calculate acoustic emission amplitude fractal dimensions of fiber-free reinforced, glass fiber reinforced, polyacrylonitrile and mixed tailing cementing material test pieces by adopting a G-P algorithm.
Further, the fiber reinforced tailing cementing material is a fiber reinforced superfine tailing cementing material, and the superfine tailing is the tailing with the particle size smaller than 20 mu m, and the mass content of the tailing is more than 50%.
According to the invention, through analyzing the damage evolution rule of the fiber reinforced superfine tailing cementing material and the acoustic emission characteristics in deformation damage, acoustic emission tests under the uniaxial compression condition are carried out by selecting different fiber reinforced superfine tailing cementing material test pieces, and the damage evolution of different fiber reinforced superfine tailing cementing materials under the action of load is analyzed from three aspects of acoustic emission energy, ringing count and acoustic emission amplitude fractal dimension; the coupling relation between the acoustic emission cumulative ringing count and the stress and damage variables is established by taking time as an intermediate quantity, the stress and damage variables of the fiber reinforced superfine tailing cementing material are calculated through the acoustic emission cumulative ringing count, and when the damage variables are close to 1, the filling body tends to be in a complete damage state; the method disclosed by the invention has high precision, can rapidly and accurately predict the damage mechanism, compressive strength and damage evolution of the fiber reinforced superfine tailing cementing material, and provides scientific reference basis for guaranteeing the mine production safety and engineering of related industries.
Drawings
FIG. 1 is a graph showing the tailing particle size distribution of a fiber-reinforced ultra-fine tailing cementing material according to an embodiment of the present invention;
FIG. 2a, FIG. 2b, FIG. 2c, FIG. 2d are graphs of stress-energy-time relationships of test pieces of different fiber-reinforced ultra-fine tailing cementing materials according to embodiments of the present invention;
FIG. 3a, FIG. 3b, FIG. 3c, FIG. 3d are graphs showing stress-ringing count-time relationships for test pieces of different fiber-reinforced ultra-fine tailing cementing materials in accordance with embodiments of the present invention;
fig. 4a, 4b, 4c and 4D are graphs of m-D dimensions of phase space of test pieces of different fiber reinforced ultra-fine tailing cementing materials according to embodiments of the present invention;
FIGS. 5a, 5b, 5c, and 5d are graphs of test pieces lnr-lnC (r) of different fiber reinforced ultra-fine tailing cementing materials according to embodiments of the present invention;
FIG. 6a, FIG. 6b, FIG. 6c, FIG. 6d are graphs of stress-time-fractal dimension for test pieces of different fiber reinforced ultra-fine tailing cementing materials in accordance with embodiments of the present invention;
FIG. 7a, FIG. 7b, FIG. 7c, FIG. 7d are graphs showing the cumulative ringing count of the failure acoustic emissions of the test piece of the different fiber reinforced ultra fine tailing cementing materials and the time according to the embodiment of the present invention;
fig. 8a, 8b, 8c and 8d are graphs comparing test curves and theoretical curves of relationships between test pieces N and sigma of different fiber reinforced ultra-fine tailing cementing materials according to embodiments of the present invention;
fig. 9a, 9b, 9c and 9D are graphs comparing test curves and theoretical curves of relationships between test pieces N and D of different fiber reinforced ultra-fine tailing cementing materials according to embodiments of the present invention;
wherein a is a fiber-free reinforced superfine tailing cementing material, b is a glass fiber-reinforced superfine tailing cementing material, c is a polyacrylonitrile fiber-reinforced superfine tailing cementing material, and d is a mixed fiber-reinforced superfine tailing cementing material.
Detailed Description
A damage analysis method of fiber reinforced superfine tailing cementing material comprises the following steps:
step one, manufacturing test pieces of different fiber reinforced superfine tailing cementing materials
In the embodiment, the tailing cementing material with the mass concentration of 65% and the sand-lime ratio of 1:6 and the glass fiber, the polyacrylonitrile fiber and the glass and polyacrylonitrile mixed fiber are respectively mixed is selected, the test piece mainly comprises tailings, cement, fiber and the like, the raw materials of the tailings are selected from tailings dams of gold mines in Henan, the distribution diagram of the particle size of the tailings is shown in figure 1, and generally, the tailings with the particle size of the tailings less than 20 μm and the content of more than 50% are ultrafine tailings. As is evident from FIG. 1, the content of the tailing particles with the particle size smaller than 20 μm used in the test is approximately 100%, which belongs to the superfine tailing. The cement adopts composite silicate cement with the code of P.C32.5, and the total amount of the admixture in the cement is more than 20% and less than 50% by mass. The fiber adopts two kinds of polyacrylonitrile fiber and glass fiber. The fiber, cement tailings and water are mixed for at least 10 minutes to obtain a homogeneous filler mixture having the desired slump. In order to avoid floating of the fibers, the fibers were added at the beginning of mixing, and the dry-mixing method was used as a method for adding the fibers, and a normal filler test piece and a fiber-doped test piece were prepared by the above method using a die having dimensions of 70.7mm×70.7mm (length×width×height) and having a slurry concentration of 65% and a mortar-to-sand ratio of 1:6, respectively. Wherein the fiber type comprises polyacrylonitrile fiber, glass fiber and a mixture of the two fibers. According to the actual condition of the mine, curing the demolded ultrafine tailing cementing material test piece for 7 days in a natural environment with the relative humidity of 95+/-5% and the temperature of 20+/-5 ℃.
Step two, performing acoustic emission test on the test piece under the condition of uniaxial compression
Table 1 shows uniaxial compression mechanical parameters of test pieces of different fiber types of cementitious materials. Wherein BL, JBX and HJB refer to glass fiber, polyacrylonitrile fiber, and glass and polyacrylonitrile fiber mixed cementing material respectively. As can be seen from Table 1, the compressive strength of the fiber-doped cementitious material test pieces was improved as compared with that of the conventional test pieces, but the degree of improvement was not the same. The compressive strength of the test pieces of the glass, the polyacrylonitrile and the mixed fiber cementing material is respectively improved by 0.059MPa, 0.301MPa and 0.077MPa compared with that of the common test pieces. It can be seen that the incorporation of the fibrous material into the ultra-fine tailings cementing material provides some reinforcement to the strength of the ultra-fine tailings cementing material. The failure mode of the test piece is defined according to the magnitude of the strain value at the time of failure, and is specifically classified into 3 types of brittle failure, brittle-ductile failure and ductile failure. (1) Brittle failure: when the stress reaches a peak value, the strain value is <1%, the residual strength is close to 0, and there is no load-bearing capacity after failure, (2) brittle-ductile failure: when the stress reaches a peak value, the strain value is between 1% and 2%, the bearing capacity is not achieved after the strain value is broken, (3) the ductility is broken: the method has the obvious initial compaction stage and the post-peak strain softening stage, and when the stress reaches the peak value, the strain value is between 1% and 5%. The test results show that the fiber reinforced superfine tailing cementing material shows an obvious initial compaction stage and a stress peak post-strain softening stage in the uniaxial compression process, and the peak strain of the test piece is between 1% and 5%, and belongs to ductile failure.
TABLE 1 uniaxial compression mechanical parameters for test pieces of cementitious materials of different mortar and mortar ratios and fiber types
As shown in fig. 2a, 2b, 2c, 2d, 3a, 3b, 3c, and 3d, the destruction process of the fiber-reinforced ultra-fine tailing cementing material is divided into 3 stages of an ascending period, a calm period and an active period by the key characteristics of the acoustic emission parameter stages. The different phase acoustic emissions have the following characteristics:
the rising period (no fiber: 0-30 s, BL: 0-30, JBX: 0-30 s, HJB: 0-75 s) is that at the initial stage of loading, scattered or small amount of energy count and acoustic emission ringing count appear in different fiber reinforced superfine tailing cementing materials, and even in a short time, no energy count and acoustic emission ringing count appear, which may be acoustic emission activity caused by transverse friction between the superfine tailing cementing material sample and the loading plate and initial pore compaction. Although the energy count and the sound emission ringing count for this period of time are small, then the energy count and the sound emission ringing count start to increase sharply once for a short time. It is clear from fig. 2a, 2b, 2c, 2d, 3a, 3b, 3c, 3d that the acoustic emission activity is intense for a short period of time, and that a small peak occurs in the energy and acoustic emission ringing count. This is because the internal pores of the test piece are gradually compacted during the stress rising phase, and some of the larger pores may be crushed. Due to the continuous friction between the tailing particles, small energy and a small ringing count are gradually generated, a large number of new microcracks are inoculated, and acoustic emission is in an ascending period.
The acoustic emission energy measurement is almost flush in the rest period (no fiber: 30-100 s, BL: 30-45 s, JBX: 30-80 s, HJB: 75-150 s), and only floats up and down in a small range, and the acoustic emission ringing count curve is approximately a straight line and slowly rises. At this stage, the internal cracks of the test piece start to sequentially expand, but the elastic strain energy accumulated in the test piece is not released, so that the acoustic emission energy count and the acoustic emission ringing count are relatively inactive, and the acoustic emission is in a calm period. Notably, not all fiber-reinforced ultra-fine tailing cementing materials have a quiet period, with a short or no quiet period. The calm period before the acoustic emission peak does not mean that the evolution of the deformation field of the superfine tailing cementing material is in a calm stage, and preparation is possibly made for the next severe evolution.
The active period (no fiber: 100-150 s, BL: 45-60 s, JBX: 80-160 s, HJB: 150-200 s) is that the acoustic emission energy amount and the acoustic emission ringing count begin to increase rapidly, because a large amount of elastic energy accumulated in the test piece is released rapidly, the crack evolution in the filler material is aggravated, a large amount of cracks are converged, penetrated and expanded, so that the whole ultra-fine tailing cementing material is unstable, and the acoustic emission is in the active period. Thus, acoustic emission events occur drastically, and energy counts and acoustic emission events increase sharply. As can be seen from fig. 2a, 2b, 2c, 2d, 3a, 3b, 3c, and 3d, the fiber reinforced ultra-fine tailing cementing material test piece has more active acoustic emission activity at this stage than the common test piece, and may have a bimodal or multimodal phenomenon.
The pulse and intermittent characteristics of multiple sudden increases and decreases of the acoustic emission energy count and the ringing count are related to better ductility of the fiber reinforced superfine tailing cementing material test piece; and the acoustic emission energy curve and the ringing count curve are bimodal or multimodal throughout the acoustic emission process. Therefore, the calm period of the fiber reinforced ultra-fine tailing cementing material can be used as precursor information of fracture, and the fracture condition can be further determined through the change of ringing count and event rate, so that the fiber reinforced ultra-fine tailing cementing material has certain research significance and value for the safety of underground stopes.
Analyzing the damage evolution of the test piece under the load action from three aspects of acoustic emission energy, ringing count and acoustic emission amplitude fractal dimension
The embodiment adopts a G-P algorithm to calculate the fractal dimension of acoustic emission amplitude of the test piece of the non-glass, polyacrylonitrile and mixed fiber reinforced superfine tailing cementing material, and the calculation method is as follows:
the time series of acoustic emission parameters can be seen as an equally spaced time series T:
T＝{t 1 ,t 2 ,t 3 ,...,t i } (1-1)
then construct an m-dimensional sub-phase space from these data, first take the first m data, determine the first point in the m-dimensional space from them, and record it as T1:
T 1 ＝{t 1 ,t 2 ,t 3 ,...,t m } (1-2)
then, T1 is removed, m data T2, T3 … and tm+1 are sequentially taken, a second point is formed by the group of data in the m-dimensional space and is denoted as T2, and a series of phase points can be formed according to the method:
the phase points T1, T2, ti. are connected in sequence to form a track. Provided with a time sequence of co-generated phase points T1, T2., TN in m-dimensional phase space, given a number r, it is checked how many pairs of points (ti, tj) have a distance i-tj less than r, and the ratio of the pairs of points having a distance less than r to the total number of pairs of points N2 is denoted C (r):
wherein: θ t Is a Heaviside function. If r gets too large, the distances of all points will not exceed it, C (r) =1, lnc (r) =0. The correlation between the phase points is not measured and if the measurement scale r is properly scaled down, there may be:
C(r)∝r D (1-5)
if such a relationship exists, D is a dimension, which is referred to as the association dimension, namely:
as shown in fig. 4a, 4b, 4c, and 4d, it is obvious that the four graphs all linearly change in the interval of the phase space dimension [3,5], so that the phase space dimension m of different fibers is uniformly taken as 4. According to the data obtained by matlab processing, lnr-lnC (r) curves and linear fitting curves of acoustic emission amplitudes of different fiber superfine tailing cementing materials are drawn, and as can be seen from fig. 5a, 5b, 5c and 5d, the linear correlation of the acoustic emission amplitudes of different fiber superfine tailing cementing materials with the fitted data curves is higher, both the acoustic emission amplitudes are higher than 0.90, and the acoustic emission amplitudes of the fiber superfine tailing cementing materials are obvious in fractal characteristics. The fractal dimension of the acoustic emission amplitude is an algorithm method disclosed in the prior art, and the acoustic emission is utilized to further research the evolution of the damage inside the filling body by combining the acoustic emission with the fractal dimension of the acoustic emission amplitude.
And according to the processing result, drawing stress-time-fractal dimension graphs of different fiber reinforced superfine tailing cementing materials by using origin software, as shown in fig. 6a, 6b, 6c and 6 d. It can be clearly seen that the amplitude fractal dimension of the fiber-free ultra-fine tailing cementing material fluctuates in a large range with increasing stress, and peaks at the peak of the stress and reaches a minimum in a period of time after the peak. This means that the fiber-free ultra-fine tailing cementing material begins to generate more irregular microcracks in the compacting stage, and the microcracks are continuously expanded and communicated with the increase of stress. After the peak, the fractal dimension thereof is greatly reduced to a minimum value, which can be used for indicating that the superfine tailing cementing material has larger damage. The fractal dimension of the test piece of the other three fiber reinforced ultrafine tailing cementing materials fluctuates up and down in a small amplitude range along with the increase of the stress, which shows that microcracks in the three fiber reinforced ultrafine tailing cementing materials continuously and stably start, expand and run through along with the increase of the stress, and finally form a macroscopic fracture surface. It is noted that the amplitude fractal dimension peaks of the fiber-free ultra-fine tailing cementing material are larger than those of other fiber-free ultra-fine tailing cementing materials, which means that the cracks in the fiber-free ultra-fine tailing cementing material are more bent and branched, so that the fiber-free ultra-fine tailing cementing material can be damaged earlier along with the increase of stress, which is consistent with the results of the previous analysis. Meanwhile, as apparent from the graph, after the fiber reinforced ultrafine tailing cementing material reaches a stress peak value, the acoustic emission fractal dimension tends to be stable and fluctuates only in a small range.
Step four, establishing a coupling relation between acoustic emission cumulative ringing count and strain by taking time as an intermediate quantity to calculate and analyze
The filling body is not damaged in a short time under the action of load, but is damaged by the structural surface formed by the initiation, expansion, collection and penetration of internal microcracks. Through the analysis, the acoustic emission ringing count of the filling body has close relation with the evolution of the internal structural defects and changes along with the change of the stress. The embodiment adopts a synchronous monitoring means of strain control and acoustic emission of a loading system, and combines a test result and a theoretical result of the former, so that the relationship between the strain and time in the loading process is as follows:
ε＝kt+ε 0
(1)
wherein epsilon is the strain of the superfine tailing cementing material and is dimensionless; k is a coefficient, and is obtained through the relation between fitting time and strain; t is the time in the loading process, and the unit is s; epsilon 0 The initial strain of the fiber reinforced superfine tailing cementing material can be obtained by linear fitting according to test data;
the relation between the cumulative ringing count N of the acoustic emission and the time t is combined and is represented by an S-shaped growth function, namely:
wherein A1, A2, B1 and B2 are constants, and the relation between fitting time and acoustic emission cumulative ringing count is directly obtained;
fitting the test result by using the formula (2), and combining the formula (1) and the formula (2) to obtain the coupling relation between the acoustic emission cumulative ringing count and the strain of the fiber reinforced superfine tailing material:
the damage constitutive model of the fiber reinforced superfine tailing cementing material is expressed as follows:
σ＝Eε(1-D) (4)
wherein: sigma is effective stress in MPa; e is the deformation modulus of the material, and the unit is MPa; epsilon is the strain; d is a damage variable;
the strength of the fiber reinforced superfine tailing cementing material is subjected to Weibull random distribution, and the probability density expression is as follows:
wherein: m, F 0 Is Weibull random distribution parameter, wherein m is shape parameter, F 0 Is a proportional parameter; f is the fiber reinforced ultra fine tailings cementing material infinitesimal strength distribution variable (either stress or strain, here strain);
definition under the condition of displacement control and loading, the damage variable D of the micro-unit of the superfine tailing cementing material is N number of damaged micro-units b Ratio to total number of mesoscopic units N:
in the interval [0,F ], the number of the microscopic units for failure of the fiber reinforced superfine tailing cementing material is any interval,
substituting the formula (7) into the formula (6) to obtain the damage variable of the fiber reinforced superfine tailing cementing material under the condition of system strain control loading:
from formula (8), the introduced mesoscopic unit strength cannot directly characterize the damage variable of the fiber reinforced ultra-fine tailing cementing material, assuming that the mesoscopic unit of the fiber reinforced ultra-fine tailing cementing material meets the maximum tensile strain yield failure criterion, i.e.
F＝f(ε)＝ε f (9)
Epsilon in f Peak strain for the fine units of fiber reinforced ultra fine tailings cementing material;
substituting the formula (9) into the formula (8) to be connected in parallel with the vertical (4), and pushing out the constitutive model of the stress-strain curve of the fiber reinforced superfine tailing cementing material as follows:
order theSimultaneous equation set resolution of m and F 0 ：
Wherein: sigma (sigma) f Peak stress in MPa; epsilon f Peak strain of a microscopic unit of the fiber reinforced superfine tailing cementing material, and alpha is the effective damage rate;
the coupling relation between the acoustic emission accumulated ringing count N of the fiber reinforced ultra-fine tailing cementing material and the stress sigma and damage variable D under the uniaxial compression condition can be obtained by the coupling type (2) and the formula (10):
and calculating stress and damage variables of the fiber-reinforced superfine tailing cementing material through acoustic emission cumulative ringing count, wherein when the damage variables are close to 1, the fiber-reinforced superfine tailing cementing material tends to be in a complete damage state.
In order to verify the correctness of the coupling relation, the strain-time and acoustic emission cumulative ringing count-time curves of different fiber reinforced superfine tailing cementing materials are respectively fitted by combining test data, and fitting parameters are shown in table 2. Substituting fitting parameters into the obtained coupling relation, drawing test curves of stress-acoustic emission cumulative ringing count and damage variable-acoustic emission cumulative ringing count of different fiber-reinforced superfine tailing cementing materials, and comparing and analyzing the test curves and fitting curves, wherein as can be seen from fig. 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d, the stress and damage variable of the fiber-reinforced superfine tailing cementing materials have higher coincidence degree with the test curves and fitting curves of acoustic emission cumulative ringing count. Therefore, under the uniaxial compression condition, the acoustic emission of the fiber reinforced superfine tailing cementing material is divided into three stages of an ascending period, a calm period and an active period, the ascending period is from the sporadic acoustic emission activity in the initial loading stage to the acoustic emission activity, the stress of the superfine tailing cementing material test piece is continuously increased along with the increase of the acoustic emission activity, and the stress peak value is reached after a period of time and enters the calm period for a short time. And then, the acoustic emission activity enters an active period, the filling body test piece enters a deformation stage after being damaged, and along with the rapid increase of the acoustic emission activity, the stress of the superfine tailing cementing material test piece begins to gradually decrease. The damage variable of the test piece of different fiber reinforced superfine tailing cementing materials gradually decreases along with the increasing slope of the acoustic emission activity, because the test piece of the superfine tailing cementing materials gradually increases along with the increasing of the stress, internal microcracks are initiated, collected, expanded and penetrated to form a damage structural surface, macroscopic damage occurs when the stress reaches a peak value, and the increasing amplitude of the damage variable is smaller. Finally, until the fiber reinforced superfine tailing cementing material test piece is completely destroyed, the damage variable tends to be 1.
TABLE 2 coupling relation parameter table of fiber-doped ultrafine tailing cementing material
The method for analyzing the coupling relation between the acoustic emission cumulative ringing count and the strain has higher precision, can rapidly and accurately predict the damage mechanism, the compressive strength and the damage evolution of the fiber reinforced superfine tailing cementing material, and provides scientific reference basis for guaranteeing the mine production safety and the engineering of related industries. The foregoing disclosure is merely illustrative of the presently preferred embodiments of the invention and is not intended to limit the scope of the claims herein, as such equivalent variations are within the scope of the invention.
Claims (5)
1. The damage analysis method of the fiber reinforced superfine tailing cementing material is characterized by comprising the following steps of:
step one, manufacturing test pieces of different fiber reinforced superfine tailing cementing materials;
step two, respectively carrying out acoustic emission tests on each test piece under the condition of uniaxial compression;
analyzing the damage evolution of the test piece under the load action from three aspects of acoustic emission energy, ringing count and acoustic emission amplitude fractal dimension;
and step four, establishing a coupling relation between acoustic emission cumulative ringing count and strain by taking time as an intermediate quantity for calculation and analysis, wherein the calculation and analysis process is as follows:
the strain control and the sound emission synchronous monitoring of the loading system are adopted, and the relationship between the strain and the time in the loading process is as follows:
ε＝kt+ε 0 (1)
wherein epsilon is the strain of the superfine tailing cementing material and has no dimension; k is a coefficient, and is obtained through the relation between fitting time and strain; t is the time in the loading process, and the unit is s; epsilon 0 The initial strain of the fiber reinforced superfine tailing cementing material can be obtained by linear fitting according to test data;
the relation between the cumulative ringing count N of the acoustic emission and the time t is combined and is represented by an S-shaped growth function, namely:
wherein A1, A2, B1 and B2 are constants, and the relation between fitting time and acoustic emission cumulative ringing count is directly obtained;
fitting the test result by using the formula (2), and combining the formula (1) and the formula (2) to obtain the coupling relation between the acoustic emission cumulative ringing count and the strain of the fiber reinforced superfine tailing cementing material:
the damage constitutive model of the fiber reinforced superfine tailing cementing material is expressed as follows:
σ＝Eε(1-D) (4)
wherein: sigma is effective stress in MPa; e is the deformation modulus of the material, and the unit is MPa; epsilon is the strain; d is a damage variable;
the strength of the fiber reinforced superfine tailing cementing material is subjected to Weibull random distribution, and the probability density expression is as follows:
wherein: m, F 0 Is Weibull random distribution parameter, wherein m is shape parameter, F 0 Is a proportional parameter; f is the infinitesimal intensity distribution variable of the fiber reinforced superfine tailing cementing material;
definition under the condition of displacement control and loading, the damage variable D of the micro-unit of the superfine tailing cementing material is N number of damaged micro-units b Ratio to total number of mesoscopic units N:
in the interval [0,F ], the number of the microscopic units for failure of the fiber reinforced superfine tailing cementing material is any interval,
substituting the formula (7) into the formula (6) to obtain the damage variable of the fiber reinforced superfine tailing cementing material under the condition of system strain control loading:
from formula (8), the introduced mesoscopic unit strength cannot directly characterize the damage variable of the fiber reinforced ultra-fine tailing cementing material, assuming that the mesoscopic unit of the fiber reinforced ultra-fine tailing cementing material meets the maximum tensile strain yield failure criterion, i.e.
F＝f(ε)＝ε f (9)
Epsilon in f Peak strain for the fine units of fiber reinforced ultra fine tailings cementing material;
substituting the formula (9) into the formula (8) to be connected in parallel with the vertical (4), and pushing out the constitutive model of the stress-strain curve of the fiber reinforced superfine tailing cementing material as follows:
order theSimultaneous equation set resolution of m and F 0 ：
Wherein: sigma (sigma) f Peak stress in MPa; epsilon f Peak strain of a microscopic unit of the fiber reinforced superfine tailing cementing material, and alpha is the effective damage rate;
the coupling relation between the acoustic emission accumulated ringing count N of the fiber reinforced ultra-fine tailing cementing material and the stress sigma and damage variable D under the uniaxial compression condition can be obtained by the coupling type (2) and the formula (10):
and calculating stress and damage variables of the fiber-reinforced superfine tailing cementing material through acoustic emission cumulative ringing count, wherein when the damage variables are close to 1, the fiber-reinforced superfine tailing cementing material tends to be in a complete damage state.
2. The method for analyzing damage of fiber reinforced superfine tailing cementing material according to claim 1, wherein the fiber reinforced superfine tailing cementing material test piece in the step one adopts cementing materials with mass concentration of 65% and cement ash-sand ratio of 1:6, and three fiber reinforced superfine tailing cementing materials of glass fiber, polyacrylonitrile fiber, glass and polyacrylonitrile mixed fiber are respectively mixed.
3. The damage analysis method for the fiber reinforced superfine tailing cementing material according to claim 1, wherein the loading strain test adopted in the acoustic emission test in the second step is a loading strain test with a loading rate of 0.5mm/min, the loading is stopped when a test piece is damaged, the sampling threshold value and the gain value of a preamplifier of acoustic emission are both 40dB, and the sensor frequency is 20-100 kHz.
4. The method of claim 1, wherein the damage evolution in step three comprises: the mechanical property analysis is used for defining the breaking modes of brittle fracture, brittle-ductile fracture and ductile fracture according to the magnitude of the strain value when the test piece is broken; the acoustic emission characteristic analysis is to respectively draw stress-energy-time and stress-ringing count-time relation graphs of different fiber reinforced superfine tailing cementing materials through received acoustic emission signal parameters, and divide the damage process into three stages of an ascending period, a calm period and an active period; and the acoustic emission fractal dimension analysis is to calculate acoustic emission amplitude fractal dimensions of fiber-free reinforced, glass fiber reinforced, polyacrylonitrile and mixed tailing cementing material test pieces by adopting a G-P algorithm.
5. The method for analyzing damage of fiber reinforced ultra-fine tailing cementing material according to claim 1, wherein the ultra-fine tailing is the tailing with the particle size smaller than 20 μm, and the mass content of the tailing is more than 50%.
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| CN112098523A (en) * | 2020-09-18 | 2020-12-18 | 玉溪矿业有限公司 | Tailing cemented filling body damage prediction system based on acoustic emission technology |
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