CN112016189B - Modification method for constitutive relation of loaded coal rock material - Google Patents
Modification method for constitutive relation of loaded coal rock material Download PDFInfo
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Abstract
The invention discloses a method for correcting constitutive relation of loaded coal-rock materials, which constructs a compaction characteristic correction model f (epsilon) of the loaded coal-rock materials based on pore structure characteristics and permeability attributes of the loaded coal-rock materials θ ) The method comprises the steps of carrying out a first treatment on the surface of the Using a modified stress-strain relationship model sigma (epsilon) θ ) And correcting the constitutive relation of the loaded coal rock material. The invention relates to a loaded coal rock material constitutive relation correction model, which has definite calculation of the related determined parameters and strong universality and operability; the modified stress-strain constitutive relation model can effectively reflect an initial compaction stage of coal rock loading, the proposed parameters can quantify the inherent physical and mechanical properties of the stage, a more reasonable damage parameter evolution rule can be revealed, and the application effect is good; finally, accurate description of the initial compaction stage of the loaded coal rock and quantitative depiction of corresponding inherent physical mechanical properties of the loaded coal rock are realized, and the method is particularly suitable for theoretical calculation, numerical simulation and engineering stability analysis in the application fields of rock mechanics and geotechnical engineering.
Description
Technical Field
The invention relates to a method for correcting constitutive relation of loaded coal rock materials.
Background
The coal-rock medium is a main structural element involved in engineering implementation processes such as underground space chamber and roadway construction, resource development and the like, and complex stress disturbance generated in the underground engineering construction process can cause deformation instability and damage of the coal-rock medium, wherein the full stress strain constitutive relation of loaded coal rock is a main key factor for understanding the coal-rock damage process.
The full-stress strain constitutive relation of the loaded coal rock comprises four stages of initial compaction, elastic deformation, plastic deformation before peak and softening deformation after peak, and a large number of scholars consider that the plastic deformation before peak and the softening deformation after peak often directly determine the catastrophe damage process of the coal rock and macroscopic damage manifestations caused by the catastrophe damage process, such as disasters of underground space collapse, ledge, rock burst and the like; meanwhile, for a compact rock material, the loaded initial compaction phenomenon is not obvious or even disappears, so that the physical mechanical process and the engineering guiding significance of the initial compaction stage are often ignored in theoretical analysis, numerical simulation calculation and engineering stability analysis application. Therefore, the method for correcting the stress-strain constitutive relation model of the existing loaded coal-rock material has very important practical value and engineering significance.
Disclosure of Invention
Aiming at the problems, the invention provides a method for correcting the constitutive relation of loaded coal rock materials, which realizes accurate description of the initial compaction stage of loaded coal rock and quantitative depiction of corresponding inherent physical mechanical properties, and is particularly suitable for theoretical calculation, numerical simulation and engineering stability analysis in the application fields of rock mechanics and geotechnical engineering.
In order to achieve the technical purpose and the technical effect, the invention is realized by the following technical scheme:
a method for correcting constitutive relation of loaded coal rock materials comprises the following steps:
construction of compaction characteristic correction model f (epsilon) of loaded coal-rock material based on pore structure characteristics and permeability properties of loaded coal-rock material θ )；
Using a modified stress-strain relationship model sigma (epsilon) θ ) Correcting constitutive relation of loaded coal rock materials, wherein:
σ(ε θ )＝f(ε θ )·σ(ε)
wherein, sigma (epsilon) θ ) For the corrected stress-strain relationship model, σ (ε) is an uncorrected stress-strain constitutive relationship model, f (ε) θ ) Is accepted asAnd correcting the compaction characteristic of the coal-bearing rock material.
Preferably:
wherein epsilon is the total strain of the loaded coal rock material θ For the initial fracture compaction stage strain of the loaded coal rock material, the exp function is an exponential function based on a natural constant e.
Preferably: initial fracture compaction stage strain epsilon for loaded coal rock material θ The calculation steps of (a) are as follows:
1) Traversing all stress-strain data points by using moving windows, wherein each moving window comprises N data points, and the x sequence of the data points in the ith moving window is { epsilon } i-N+1 ,…,ε i-1 ,ε i Y sequence { sigma }, y sequence i-N+1 ,…,σ i-1 ,σ i Stiffness modulus E corresponding to the moving window i The method comprises the following steps:
in the method, in the process of the invention,
average value of x and y sequences, x k To move the x sequence, y of data points within the window k Y-sequence of data points within a moving window;
2) Plotting the modulus of rigidity E i Along with stress sigma i Finding stress value sigma corresponding to initial mutation point in curve θ The corresponding strain is the strain value epsilon of the initial fracture compaction stage of the loaded coal rock material θ 。
Preferably: n is in the range of 20-50, for example, N is 35.
Preferably: according to modulus of rigidity E i Along with stress sigma i Selecting a stiffness modulus data point of a stationary curve stage after an initial abrupt point,calculating the average value as the elastic modulus E, and then the uncorrected stress-strain constitutive relation model sigma (epsilon) is as follows:
wherein D is a damage parameter, m and F are damage parameters, E is an elastic modulus,
for plastic strain, σ is the experimentally measured stress value.
Preferably: m and F are obtained through fitting experimental data.
The beneficial effects of the invention are as follows:
the loaded coal rock material constitutive relation correction model has obvious physical and mechanical significance, definite calculation of the determined parameters involved in the parameters and strong universality and operability; the modified stress-strain constitutive relation model can effectively reflect an initial compaction stage of coal rock loading, the proposed parameters can quantify the inherent physical and mechanical properties of the stage, a more reasonable damage parameter evolution rule can be revealed, and the application effect is good; the invention has very important significance for perfecting the coal rock stress strain constitutive relation model used in the prior theoretical calculation, numerical simulation and engineering stability analysis, and finally realizes the accurate description of the initial compaction stage of the loaded coal rock and the quantitative depiction of the corresponding inherent physical mechanical properties, and is particularly suitable for the theoretical calculation, the numerical simulation and the engineering stability analysis in the application fields of rock mechanics and geotechnical engineering.
Drawings
FIG. 1 is a schematic diagram showing a typical uniaxial compression full-stress strain experimental curve of coal rock, and comparing the results of a damage statistics constitutive theoretical model with the results of a correction model of the invention;
FIG. 2 is a schematic diagram of a calculation of a linear regression method for data points of a moving window employed in the present invention;
FIG. 3 shows the calculation process and results of strain εθ and elastic modulus at initial fracture compaction stage in accordance with one embodiment of the present invention;
FIG. 4 shows the initial fracture compaction stage strain ε in a second embodiment of the invention θ And the calculation process and result of the elastic modulus;
fig. 5 is a schematic diagram showing the comparison of the calculation results before and after correction in the second embodiment of the present invention.
Detailed Description
The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples, so that those skilled in the art can better understand the present invention and implement it, but the examples are not limited thereto.
Studies have shown that the essential cause of the initial compaction stage is the compaction closure of pre-existing raw pore cracks in the coal rock medium material under load, whereas the raw pore structure of the coal rock medium is critical in determining the coal rock permeability properties and the time of deformation of the coal rock under load. Therefore, the inherent physical and mechanical properties of the initial compaction stage are researched, so that the stress strain constitutive model of the existing loaded coal-rock material is corrected, the inherent properties of the coal-rock medium material are depicted, and the method has very important practical value and engineering significance.
Method for correcting constitutive relation of loaded coal-rock material, and construction of compaction characteristic correction model f (epsilon) of loaded coal-rock material based on pore structure characteristics and permeability properties of loaded coal-rock material θ )；
The pore structure characteristics include, among other things, pore and throat types, sizes, distributions and interconnections within the rock, and the ability of the rock to be permeated by fluids is referred to as the permeability of the rock.
Using a modified stress-strain relationship model sigma (epsilon) θ ) Correcting constitutive relation of loaded coal rock materials, wherein:
σ(ε θ )＝f(ε θ )·σ(ε)
wherein, sigma (epsilon) θ ) For the corrected stress-strain relationship model, σ (ε) is an uncorrected stress-strain constitutive relationship model, f (ε) θ ) The model is modified for compaction characteristics of the loaded coal rock material.
Preferably:
wherein epsilon is the total strain of the loaded coal rock material θ For the initial fracture compaction stage strain of the loaded coal rock material, the exp function is an exponential function based on a natural constant e.
Initial fracture compaction stage strain ε θ The elastic modulus E can be determined by calculation using a moving window data point linear regression method, which is described below.
Preferably: initial fracture compaction stage strain epsilon for loaded coal rock material θ The calculation steps of (a) are as follows:
1) The moving windows are used to traverse all stress-strain data points, and each moving window is set to contain N data points, wherein the value of N is generally 20-50, and is related to the sampling frequency, for example, the value of N is 35. Wherein the x sequence of data points in the ith moving window is { ε } i-N+1 ,…,ε i-1 ,ε i Y sequence { sigma }, y sequence i-N+1 ,…,σ i-1 ,σ i Stiffness modulus E corresponding to the moving window i The method comprises the following steps:
in the method, in the process of the invention,
average value of x and y sequences, x k To move the x sequence, y of data points within the window k Y-sequence of data points within a moving window;
2) Plotting the modulus of rigidity E i Along with stress sigma i Finding stress value sigma corresponding to initial mutation point in curve θ The corresponding strain is the strain value epsilon of the initial fracture compaction stage of the loaded coal rock material θ 。
Preferably: according to modulus of rigidity E i Along with stress sigma i And (3) selecting stiffness modulus data points in a stationary curve stage after an initial abrupt point, and calculating an average value of stiffness modulus data points as an elastic modulus E.
According to the theoretical model such as the statistical damage mechanism and the numerical simulation model:
σ(ε θ )＝f(ε θ )·σ(ε)
according to the reliability theory, the compaction characteristic correction model f (epsilon) of the loaded coal rock material θ ) Has obvious physical meaning, wherein epsilon θ Corresponding to the average lifetime of the finger distribution in reliability theory,
indicating failure rate and therefore epsilon θ Also known as pore compaction average strain->
Also known as void failure rate.
Taking a damage statistics constitutive theoretical model as an example: the uncorrected stress-strain constitutive relation model σ (ε) is:
wherein D is a damage parameter, m and F are damage parameters, which can be obtained by fitting experimental data, E is an elastic modulus,
for plastic strain, σ is the experimentally measured stress value.
The compaction characteristic correction model f (epsilon) of the loaded coal rock material is introduced θ ) Then the corrected stress-strain relation model sigma (epsilon) θ ) The method comprises the following steps:
the evolution rule of the damage parameters can be obtained by fitting experimental data: parabolic growth of the initial fracture compaction stage, retention of the elastic stage, slow growth of the pre-peak plastic stage, and a sharp rise of the post-peak softening stage.
The invention is further described by taking a coal rock uniaxial compression full-stress strain experimental curve and a damage statistics constitutive theory model as examples with reference to the accompanying drawings.
As shown in FIG. 1, a typical uniaxial compressive full stress strain experimental curve of coal rock is shown, and the whole coal rock loading deformation and damage process comprises an initial fracture closure 0A stage, an elastic AB stage, a pre-peak plasticity BC stage and a post-peak CD stage.
Taking a damage statistics constitutive theoretical model as an example, the calculation formula is as follows:
wherein D is an injury parameter; m and F are damage parameters, and experimental data fitting is adopted to obtain the damage parameters; sigma (epsilon) is a stress-strain constitutive relation model of which the damage statistics constitutive theory is not corrected; e is the elastic modulus; epsilon is the total strain;
for plastic strain, σ is the experimentally measured stress value.
The compaction characteristic correction model f (epsilon) of the loaded coal rock material is introduced θ ) Then the corrected stress-strain relation model sigma (epsilon) θ ) The method comprises the following steps:
taking the typical uniaxial compression full stress strain experimental curve of coal and rock as shown in fig. 1 as an example, the first embodiment of the invention is implemented according to the idea of the invention:
(1) The linear regression method of the moving window data points as shown in fig. 2 is used to calculate the linear fitting slope of all stress-strain data points in each moving window as the stiffness modulus of the moving window and corresponds to the last data point in the moving window.
(2) The stiffness moduli of all the moving windows and the corresponding stress values thereof are connected in sequence, and a stiffness modulus-stress curve shown in fig. 3 is drawn.
(3) Picking up stress value sigma corresponding to the initial abrupt point in the stiffness modulus-stress curve θ As shown in FIG. 3, and acquires the corresponding strain ε θ =0.006 is the initial fracture compaction stage strain value.
(4) Further, stiffness modulus data points at a plateau after the initial abrupt point are selected, and as shown in fig. 3, the average value thereof is calculated as a value of e=2720mpa of elastic modulus.
(5) From the experimentally measured stress-strain data points (. Epsilon.,. Sigma.) the formula is used
The plastic strain corresponding to each data point was calculated as shown in fig. 1.
(6) Will epsilon θ E and ε p Substituting formula (3) and obtaining the damage parameters m=1.996, f=0.008, and the corrected model results of the present invention by fitting experimental data, as shown in fig. 1.
(7) Will epsilon p And m and F are substituted into the formula (1) to obtain the damage parameter curve shown in figure 1.
(8) E, m and F were substituted into formula (2) to obtain an uncorrected model result curve as shown in fig. 1.
As can be seen from FIG. 1, the correlation coefficient between the corrected model result and the experimental result of the present invention is as high as 0.9996, which is significantly better than the uncorrected model result; meanwhile, the damage parameters obtained by the method are parabolic in the initial fracture compaction 0A stage, the elastic AB stage is kept unchanged, the pre-peak plasticity BC stage is slowly increased, the post-peak softening CD stage is rapidly increased, and the evolution rule is more reasonable.
Similarly, referring to the comparative results of the second embodiment of the present invention shown in fig. 4-5, the comparative list of the corrected result and the uncorrected result obtained by the correction method of the present invention is shown in the following table 1, and the greater the correlation coefficient in the table, the better the model fitting effect is illustrated by the comparative verification of the correlation coefficient fitted with the experimental result; if the correlation coefficient is 1, the model result is completely matched with the experimental result. It can be seen from table 1 that the modified model results of the present invention are significantly better than the unmodified model results.
TABLE 1 comparison of modified vs. unmodified results of the invention
| Correlation coefficient fitting to experimental results | The invention corrects the model result | Uncorrected model results |
| Description of the preferred embodiments | 0.9996 | 0.9819 |
| Second embodiment | 0.9974 | 0.9802 |
In conclusion, the physical meaning and the calculation process of each parameter related by the invention are clear, the universality and the operability are strong, and the corrected model result can be goodIs fit to the experimental results. Thus, the model f (. Epsilon.) proposed by the present invention θ ) The compaction characteristic general correction model can be used for correcting the constitutive relation of the loaded coal and rock material, can be particularly applied to the research fields of theoretical analysis, numerical calculation and the like, and finally can realize accurate description of the initial compaction stage of the loaded coal and quantitative characterization of corresponding inherent physical mechanical properties, and is particularly suitable for theoretical calculation, numerical simulation and engineering stability analysis in the application fields of rock mechanics and geotechnical engineering.
The foregoing description is only of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, but rather is intended to cover any equivalents of the structures disclosed herein or modifications in equivalent processes, or any application, directly or indirectly, within the scope of the invention.
Claims (5)
1. A method for correcting the constitutive relation of loaded coal rock materials is characterized by comprising the following steps:
construction of compaction characteristic correction model f (epsilon) of loaded coal-rock material based on pore structure characteristics and permeability properties of loaded coal-rock material θ )；
Using a modified stress-strain relationship model sigma (epsilon) θ ) Correcting constitutive relation of loaded coal rock materials, wherein:
σ(ε θ )＝f(ε θ )·σ(ε)
wherein, sigma (epsilon) θ ) For the corrected stress-strain relationship model, σ (ε) is an uncorrected stress-strain constitutive relationship model, f (ε) θ ) Correcting the model for compaction characteristics of the loaded coal rock material;
wherein:
wherein epsilon is the total strain of the loaded coal rock material θ The method is characterized in that strain in an initial fracture compaction stage of a loaded coal rock material is obtained, and an exp function is an exponential function based on a natural constant e;
initial fracture compaction stage strain epsilon for loaded coal rock material θ The calculation steps of (a) are as follows:
1) Traversing all stress-strain data points by using moving windows, wherein each moving window comprises N data points, and the x sequence of the data points in the ith moving window is { epsilon } i-N+1 ,…,ε i-1 ,ε i Y sequence { sigma }, y sequence i-N+1 ,…,σ i-1 ,σ i Stiffness modulus E corresponding to the moving window i The method comprises the following steps:
in the method, in the process of the invention,
average value of x and y sequences, x k To move the x sequence, y of data points within the window k Y-sequence of data points within a moving window;
2) Plotting the modulus of rigidity E i Along with stress sigma i Finding stress value sigma corresponding to initial mutation point in curve θ The corresponding strain is the strain value epsilon of the initial fracture compaction stage of the loaded coal rock material θ 。
2. The method for modifying the constitutive relation of a loaded coal rock material according to claim 1, wherein: the value range of N is 20-50.
3. The method for modifying the constitutive relation of a loaded coal rock material according to claim 2, wherein:
n is 35.
4. The method for modifying the constitutive relation of a loaded coal rock material according to claim 1, wherein: according to modulus of rigidity E i Along with stress sigma i Selecting the stiffness modulus of the stationary curve stage after the initial abrupt pointData points, the average value of which is calculated as the elastic modulus E, the uncorrected stress-strain constitutive relation model sigma (epsilon) is:
wherein D is a damage parameter, m and F are damage parameters, E is an elastic modulus,
in order to be a plastic strain,
sigma is the experimentally measured stress value.
5. The method for modifying the constitutive relation of a loaded coal rock material according to claim 4, wherein:
m and F are obtained through fitting experimental data.
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| CN110006759A (en) * | 2019-04-12 | 2019-07-12 | 西安建筑科技大学 | Determine the method that different osmotic power influences the deformation of uniaxial compression limestone densification stage |
| CN110705165A (en) * | 2019-10-08 | 2020-01-17 | 中国石油大学(华东) | Method for constructing elastoplasticity-damage coupling mechanical constitutive model of rock material |
| CN111323562A (en) * | 2020-04-16 | 2020-06-23 | 河海大学 | Method for establishing fracture-filled rock seepage damage softening model |
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| CN110006759A (en) * | 2019-04-12 | 2019-07-12 | 西安建筑科技大学 | Determine the method that different osmotic power influences the deformation of uniaxial compression limestone densification stage |
| CN110705165A (en) * | 2019-10-08 | 2020-01-17 | 中国石油大学(华东) | Method for constructing elastoplasticity-damage coupling mechanical constitutive model of rock material |
| CN111323562A (en) * | 2020-04-16 | 2020-06-23 | 河海大学 | Method for establishing fracture-filled rock seepage damage softening model |
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| 周科平等."不同渗透力的类充填体力学特性及损伤软化本构模型研究".《岩土力学》.2019,第40卷(第10期),摘要和第3725页第1栏第2行至第3728页第2栏第29行. * |
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