CN113405906A - Method for establishing damage model of initial damage-containing cemented filling body - Google Patents
Method for establishing damage model of initial damage-containing cemented filling body Download PDFInfo
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- CN113405906A CN113405906A CN202110681095.8A CN202110681095A CN113405906A CN 113405906 A CN113405906 A CN 113405906A CN 202110681095 A CN202110681095 A CN 202110681095A CN 113405906 A CN113405906 A CN 113405906A
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- 238000000034 method Methods 0.000 title claims abstract description 29
- 230000008878 coupling Effects 0.000 claims abstract description 24
- 238000010168 coupling process Methods 0.000 claims abstract description 24
- 238000005859 coupling reaction Methods 0.000 claims abstract description 24
- 230000009471 action Effects 0.000 claims abstract description 14
- 238000007906 compression Methods 0.000 claims abstract description 14
- 230000006835 compression Effects 0.000 claims abstract description 11
- 239000003795 chemical substances by application Substances 0.000 claims description 14
- 238000009826 distribution Methods 0.000 claims description 7
- 238000012669 compression test Methods 0.000 claims description 5
- 239000000945 filler Substances 0.000 claims description 3
- 239000000126 substance Substances 0.000 claims description 3
- 238000004519 manufacturing process Methods 0.000 abstract description 3
- 239000011435 rock Substances 0.000 abstract description 3
- 230000000694 effects Effects 0.000 abstract description 2
- 238000012360 testing method Methods 0.000 description 13
- 239000000463 material Substances 0.000 description 12
- 230000007547 defect Effects 0.000 description 8
- 238000005259 measurement Methods 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 238000009825 accumulation Methods 0.000 description 1
- 239000004568 cement Substances 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000005056 compaction Methods 0.000 description 1
- 238000001035 drying Methods 0.000 description 1
- 230000036571 hydration Effects 0.000 description 1
- 238000006703 hydration reaction Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000005065 mining Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 238000012856 packing Methods 0.000 description 1
- 239000002245 particle Substances 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 230000001360 synchronised effect Effects 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/02—Details
- G01N3/06—Special adaptations of indicating or recording means
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- G—PHYSICS
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Abstract
The invention discloses a method for establishing a damage model of a cemented filling body containing initial damage, which comprises the following steps of firstly, establishing an initial damage equation of the cemented filling body containing the initial damage; secondly, establishing a load damage variable function considering a damage threshold; thirdly, determining a damage constitutive equation of the initial damage-containing cemented filling body under the action of load; fourthly, establishing the constitutive relation of the cemented filling body in the initial damage and load damage coupling state; fifthly, determining a total damage variable equation of the cemented filling body containing the initial damage in the coupling state; sixthly, establishing a total damage evolution equation of the cemented filling body containing the initial damage under the compression condition; and seventhly, establishing a damage model of the initial damage-containing cemented filling body. The method has reasonable steps, deduces and establishes the damage model containing the initial damage cemented filling body, provides scientific reference basis for effectively utilizing the tailing cemented filling body to maintain the stability of the surrounding rock of the goaf and guarantee the safe production, has obvious effect and is convenient to popularize.
Description
Technical Field
The invention belongs to the technical field of mine filling mining, and particularly relates to a method for establishing a damage model of a cemented filling body containing initial damage.
Background
In the mine filling engineering practice, a cemented filling body material is fully mixed by a stirrer and then is transported to an underground goaf by a pipeline, the cemented filling body is usually used for temporarily or permanently supporting the goaf, the mechanical properties of the cemented filling body are similar to those of concrete, for example, initial defects such as air bubbles, holes, microcracks, micropores and the like are easily caused in the filling body material due to water seepage, drying shrinkage, hydration heat of cement and the like in the preparation process and the hardening process of the cemented filling body, and the initial defects control the damage mechanism of the brittle material and determine the structural strength of the brittle material. Therefore, the initial defect test is carried out on the cemented filling material, and the establishment of the damage mechanical model containing the initial damage parameters has important theoretical and practical significance on the stability of the underground mine goaf.
In the prior art, when a study is made on brittle materials such as rock and concrete, the materials are generally treated as if no initial defect exists inside the materials. According to the theory of continuous damage mechanics, it is known that the direct measurement of the initial damage variable is very difficult, so that no one has detailed quantitative measurement of the distribution of the initial defects of the brittle material, and a reasonable damage model building method of the cemented filling body containing the initial defects is lacked.
Disclosure of Invention
The invention aims to solve the technical problem that the defects in the prior art are overcome, and the method for establishing the damage model of the cemented filling body with the initial damage is provided.
In order to solve the technical problems, the invention adopts the technical scheme that: a method for establishing a damage model of a cemented filling body containing initial damage comprises the following steps:
step one, establishing an initial damage equation of the cemented filling body containing initial damage through a uniaxial compression test;
secondly, according to the strain equivalence theorem and the randomness of infill infinitesimal, a loaded damage variable function considering a damage threshold value is established by combining a damage probability model based on Weibull distribution;
step three, determining a damage constitutive equation of the initial damage-containing cemented filling body under the action of load;
step four, combining the initial damage equation of the cemented filling body with the initial damage and the damage constitutive equation of the cemented filling body with the initial damage under the load action, and establishing the constitutive relation of the cemented filling body with the initial damage and the load damage in a coupling state;
fifthly, determining a total damage variable equation of the cemented filling body containing the initial damage in the coupling state;
step six, combining the initial damage equation of the initial damage-containing cemented filling body, the damage constitutive equation of the initial damage-containing cemented filling body under the load action, and the total damage variable equation of the initial damage-containing cemented filling body under the coupling state; establishing a total damage evolution equation of the initial damage-containing cemented filling body under a compression condition;
step seven, combining the constitutive relation of the cemented filling body with the initial damage and the load damage in the coupling state, a total damage variable equation of the cemented filling body with the initial damage in the coupling state, and a total damage evolution equation of the cemented filling body with the initial damage in the compression condition; and establishing a damage model of the initial damage-containing cemented filling body.
In the method for establishing the damage model of the initial damage-containing cemented filling body, in the first step, the initial damage equation of the initial damage-containing cemented filling body is as follows:
wherein D isiniInitial damage to cemented filling bodies containing initial damage, EiniIs the elastic modulus in the initial damaged state, E0The modulus of elasticity in the intact state.
In the method for establishing the damage model of the cemented filling body containing the initial damage, the load damage variable function considering the damage threshold in the second step is as follows:
wherein D issIs the damage variable under load, and epsilon is the strain of the cemented filling body under uniaxial compression0And m represents a distribution parameter, gamma is damage threshold strain, 0 is taken as the gamma of the cemented filling body without the air entraining agent, and 0.25 epsilon is taken as the gamma of the cemented filling body with the air entraining agentf，εfThe strain value corresponding to the peak stress on the stress-strain curve of the cementitious filler.
In the method for establishing the damage model of the initial damage-containing cemented filling body, in the third step, the damage constitutive equation of the initial damage-containing cemented filling body under the load action is as follows:
where σ represents stress.
In the method for establishing the damage model of the cemented filling body containing the initial damage, the constitutive relation of the cemented filling body in the initial damage and load damage coupling state in the fourth step is as follows:
in the method for establishing the damage model of the cemented filling body with the initial damage, in the step five, the variable equation of the total damage of the cemented filling body with the initial damage in the coupling state is as follows:
wherein D is the total damage variable of the cemented filling body containing the initial damage in the coupling state.
In the method for establishing the damage model of the initial damage-containing cemented filling body, in the sixth step, the evolution equation of the total damage of the initial damage-containing cemented filling body under the compression condition is as follows:
in the method for establishing the damage model of the initial damage-containing cemented filling body, in the seventh step, the damage model of the initial damage-containing cemented filling body is as follows:
wherein the content of the first and second substances,
in the formula, σfFor cementing containing initial damagePeak stress of the pack.
Compared with the prior art, the invention has the following advantages: the method provided by the invention has simple and reasonable steps, the initial damage equation of the cemented filling body with the initial damage is determined through uniaxial compression and a synchronous acoustic emission monitoring test, the damage model of the cemented filling body with the initial damage is deduced and established by combining a strain equivalence theorem, a scientific reference basis can be provided for mine enterprises to more effectively utilize the tailing cemented filling body to maintain the stability of the surrounding rock of the goaf and guarantee safe production, the effect is obvious, and the popularization is convenient.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a graph showing the evolution of the damage of a cemented filling body according to the invention at different initial damage levels;
FIG. 3 is a graph comparing theoretical curves and experimental curves of a damage model of the present invention.
Detailed Description
As shown in fig. 1, the method for establishing a damage model of a cemented filling body containing initial damages comprises the following steps:
step one, establishing an initial damage equation of the cemented filling body containing initial damage through a uniaxial compression test:
wherein D isiniInitial damage to cemented filling bodies containing initial damage, EiniIs the elastic modulus in the initial damaged state, E0The modulus of elasticity in the intact state.
Step two, according to the strain equivalence theorem and the randomness of infill elements, and in combination with a damage probability model based on Weibull distribution, determining a load damage variable function considering a damage threshold value:
σ＝(1-Ds)E0ε；
wherein D issIs the damage variable under load, and epsilon is the strain of the cemented filling body under uniaxial compression0And m represents a distribution parameter, gamma is damage threshold strain, 0 is taken as the gamma of the cemented filling body without the air entraining agent, and 0.25 epsilon is taken as the gamma of the cemented filling body with the air entraining agentf，εfThe strain value corresponding to the peak stress on the stress-strain curve of the cementitious filler.
In specific implementation, to establish a reasonable damage model of the cemented filling body, initial defects generated by a manufacturing process of the filling body and the like must be considered, the influence of initial damages of different degrees on the mechanical properties of the cemented filling body is considered, because the cemented filling body always has initial damages such as initial microcracks, micro cavities and the like, the elastic modulus before the cemented filling body is not known or is not measurable, and the direct measurement of damage variables can be known to be very difficult according to a continuous damage mechanical theory, therefore, the damage model is realized by adopting a strain equivalence hypothesis (the damaged deformation of the material can be reflected by effective stress), namely, the constitutive relation of the damaged material can be in a lossless mode, and then the stress in the damaged material is replaced by the effective stress.
Step three, determining a damage constitutive equation of the initial damage-containing cemented filling body under the action of load:
where σ represents stress.
Step four, combining the initial damage equation of the cemented filling body with the initial damage and the damage constitutive equation of the cemented filling body with the initial damage under the load action, and establishing the constitutive relation of the cemented filling body with the initial damage and the load damage in a coupling state:
step five, determining a total damage variable equation of the cemented filling body containing the initial damage under the coupling state:
wherein D is the total damage variable of the cemented filling body containing the initial damage in the coupling state.
Step six, combining the initial damage equation of the initial damage-containing cemented filling body, the damage constitutive equation of the initial damage-containing cemented filling body under the load action, and the total damage variable equation of the initial damage-containing cemented filling body under the coupling state; establishing a total damage evolution equation of the initial damage-containing cemented filling body under a compression condition:
step seven, combining the constitutive relation of the cemented filling body with the initial damage and the load damage in the coupling state, a total damage variable equation of the cemented filling body with the initial damage in the coupling state, and a total damage evolution equation of the cemented filling body with the initial damage in the compression condition; establishing a damage model of the initial damage-containing cemented filling body:
wherein the content of the first and second substances,
in the formula, σfThe peak stress of the cemented filling containing initial damage.
In order to verify the rationality of the damage model of the cemented filling body containing initial damage, a cemented filling body test piece containing initial damage is prepared, a single-axis compression test and damage evolution analysis are carried out on the cemented filling body test piece by adopting an MTS microcomputer control electronic universal tester, in order to reflect the influence of the initial damage of the cemented filling body, air entraining agents with different percentage contents are doped in the pouring process of the cemented filling body test piece, different initial damage degrees of the cemented filling body are reflected through different doping amounts of the air entraining agents, and the damage evolution curve of the cemented filling body with different initial damage degrees is shown in figure 2.
As can be seen from fig. 2, the change laws of the damage of the cemented filling bodies with different initial damage degrees under the condition of uniaxial compression all have similar laws, namely, the damage is slowly increased in the initial stage of loading; with the increase of the load, the strain energy stored in the cemented filling body is gradually released, the damage is further increased, and a rapid growth stage is entered; and then the compressive stress reaches the peak value, the test piece is damaged, the damage growth rate is slowed down until the test piece completely loses the strength, and the damage accumulation also reaches 1. For the cemented filling bodies with different amounts of the air entraining agent, under the load action, the damage is slowly increased from the initial damage value, and the damage value reaches 1 after the slow increase stage, the accelerated increase stage and the accelerated slow decrease stage. For cemented packings incorporating different levels of air entraining agent, the damage evolution curve develops from different initial damages as a result of the different initial damages. In the slow growth stage, under the load action of the cemented filling body, the skeleton particles of the part which is not affected by the air entraining agent begin to deform towards the adjacent empty area of the cavity generated by the air entraining agent, and the cemented filling body is in the compaction stage, so that the damage is slowly increased; in the accelerated growth stage, due to the existence of initial damage, the test piece is subjected to pull damage and shear damage originating from a cavity generated by an air entraining agent until the peak strength of the test piece is reached; and a damage speed increasing and slowing stage, namely, a test piece is damaged and enters a post-peak stage, and damage is continuously accumulated until the damage speed reaches 1. The test phenomenon is highly consistent with the damage model of the initial damage-containing cemented filling body established by the invention, and the model has certain rationality.
In order to further verify the rationality and the correctness of the damage model of the initial damage-containing cemented filling body, the obtained damage statistical parameters were substituted into the damage model, theoretical curves of Air Entraining Agents (AEA) with different percentage contents were respectively drawn and compared with the respective compression test curves, and the results are shown in fig. 3.
From the figure 3, it can be seen that from the trend of the damage model theoretical curve and the test curve, the damage model theoretical curve can better represent the deformation and damage process of the cemented filling body, and the damage model theoretical curve and the test curve show good consistency, which illustrates the rationality of the damage model of the cemented filling body containing initial damage of the invention.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims (8)
1. A method for establishing a damage model of a cemented filling body containing initial damage is characterized by comprising the following steps:
step one, establishing an initial damage equation of the cemented filling body containing initial damage through a uniaxial compression test;
secondly, according to the strain equivalence theorem and the randomness of infill infinitesimal, a loaded damage variable function considering a damage threshold value is established by combining a damage probability model based on Weibull distribution;
step three, determining a damage constitutive equation of the initial damage-containing cemented filling body under the action of load;
step four, combining the initial damage equation of the cemented filling body with the initial damage and the damage constitutive equation of the cemented filling body with the initial damage under the load action, and establishing the constitutive relation of the cemented filling body with the initial damage and the load damage in a coupling state;
fifthly, determining a total damage variable equation of the cemented filling body containing the initial damage in the coupling state;
step six, combining the initial damage equation of the initial damage-containing cemented filling body, the damage constitutive equation of the initial damage-containing cemented filling body under the load action, and the total damage variable equation of the initial damage-containing cemented filling body under the coupling state; establishing a total damage evolution equation of the initial damage-containing cemented filling body under a compression condition;
step seven, combining the constitutive relation of the cemented filling body with the initial damage and the load damage in the coupling state, a total damage variable equation of the cemented filling body with the initial damage in the coupling state, and a total damage evolution equation of the cemented filling body with the initial damage in the compression condition; and establishing a damage model of the initial damage-containing cemented filling body.
2. The method for establishing the damage model of the initial damage-containing cemented filling body according to claim 1, wherein the initial damage equation of the initial damage-containing cemented filling body in the first step is as follows:
wherein D isiniInitial damage to cemented filling bodies containing initial damage, EiniIs the elastic modulus in the initial damaged state, E0The modulus of elasticity in the intact state.
3. The method for establishing the damage model of the cemented filling body containing the initial damage according to claim 2, wherein the variable function of the load damage considering the damage threshold in the second step is as follows:
wherein D issIs the damage variable under load, and epsilon is the strain of the cemented filling body under uniaxial compression0And m represents a distribution parameter, gamma is damage threshold strain, 0 is taken as the gamma of the cemented filling body without the air entraining agent, and 0.25 epsilon is taken as the gamma of the cemented filling body with the air entraining agentf，εfThe strain value corresponding to the peak stress on the stress-strain curve of the cementitious filler.
4. The method for establishing the damage model of the initial damage-containing cemented filling body according to claim 3, wherein the damage constitutive equation of the initial damage-containing cemented filling body under the loading action in the step three is as follows:
where σ represents stress.
5. The method for establishing the damage model of the cemented filling body containing the initial damage according to claim 4, wherein the constitutive relation of the cemented filling body in the coupling state of the initial damage and the load damage in the fourth step is as follows:
6. the method for establishing the damage model of the cemented filling body containing the initial damage according to claim 5, wherein the variable equation of the total damage of the cemented filling body containing the initial damage in the coupling state in the fifth step is as follows:
wherein D is the total damage variable of the cemented filling body containing the initial damage in the coupling state.
7. The method for establishing the damage model of the initial damage-containing cemented filling body according to claim 6, wherein the evolution equation of the total damage of the initial damage-containing cemented filling body under the compression condition in the sixth step is as follows:
8. the method for establishing the damage model of the initial damage-containing cemented filling body according to claim 7, wherein the damage model of the initial damage-containing cemented filling body in the seventh step is as follows:
wherein the content of the first and second substances,
in the formula, σfThe peak stress of the cemented filling containing initial damage.
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