CN116499881A - Method for establishing rock theoretical damage evolution model - Google Patents
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Abstract
The application relates to a method for establishing a rock theoretical damage evolution model, and relates to the technical field of underground engineering. The method comprises the following steps: determining a second damage unit number expression of the damage unit developing along with the strain based on the Torpedo model and the first damage unit number expression of the damage unit developing along with the strain in the rock sample to be tested; determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression; carrying out a uniaxial compression test on a rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, determining a third damage variable expression, further determining damage variables corresponding to each strain of the rock sample to be tested according to test results, carrying out linear fitting according to the second damage variable expression, determining each parameter in the second damage variable expression, and further obtaining a rock theoretical damage evolution model. By adopting the method, the rock theoretical damage evolution model can be established.
Description
Technical Field
The application relates to the technical field of underground engineering, in particular to a method for establishing a rock theoretical damage evolution model.
Background
At present, as the exploitation of underground solid mineral resources is advanced from shallow parts to deep spaces gradually, the complex geological environments such as high ground stress, high ground temperature, high osmotic pressure, strong excavation disturbance and the like faced by deep rock engineering lead to irreversible development of internal defects of rock, the damage degree is accumulated in a nonlinear manner, and disaster accidents such as rock burst, rock burst and the like are extremely easy to occur. The process of damaging and breaking the inside of the rock is accompanied by energy dissipation, and the probability and intensity of rock burst occurrence are closely related to the process of storing, dissipating and releasing the energy inside the rock. The deep research of the rock damage development rule has important significance for monitoring the stability, controlling the deformation and early warning the disaster of the surrounding rock of the deep underground engineering.
Therefore, a method for establishing a rock theoretical damage evolution model is needed.
Disclosure of Invention
Based on this, it is necessary to provide a method for establishing a rock theoretical damage evolution model aiming at the technical problems. The method comprises the following steps:
determining a second damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain, based on the Torpedo model and the first damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain; the first damage unit number expression is constructed based on the growth rate of damage units in the rock sample to be detected along with the strain development, the growth rate of the damage units in the rock sample to be detected and the number of the damage units at the last strain moment in the rock sample to be detected;
determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression; the first damage variable expression is constructed based on a number of breaking units in the rock sample to be tested and a total number of rock units in the rock sample to be tested;
carrying out a uniaxial compression test on the rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, and determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested;
and determining a damage variable corresponding to each strain of the rock sample to be tested according to the third damage variable expression, and performing linear fitting according to the second damage variable expression to determine a rock theoretical damage evolution model.
As an alternative embodiment, the first expression of the number of breaking units of the rock sample to be tested, which develops along with the strain, is:
dv/dε=r(v)v；
wherein dv/dε is the growth rate of the number of the breaking units in the rock sample to be tested along with the strain development, v is the number of the breaking units in the rock sample to be tested at the last strain moment, and r (v) is a function of the number v of the breaking units in the rock sample to be tested at the last strain moment, and represents the growth rate of the breaking units in the rock sample to be tested.
As an alternative embodiment, the second expression of the number of breaking units of the breaking unit that develops with strain is:
dv/dε=-aln(v/k)v；
wherein dv/dε is the growth rate of the breaking units in the rock sample to be tested along with the strain development of the rock sample to be tested, a is a first model parameter, v is the number of the breaking units in the rock sample to be tested, and k is the total number of the rock units in the rock sample to be tested.
As an alternative embodiment, the first impairment variable expression is:
D=v/k；
wherein D is a damage variable of the rock sample to be tested, v is the number of damage units in the rock sample to be tested, and k is the total number of rock units in the rock sample to be tested.
As an alternative embodiment, the second injury variable expression is:
D=exp[-exp(b-aε)]；
wherein D is a damage variable of the rock sample to be tested, a is a first model parameter, b is a second model parameter, and epsilon is the strain of the rock sample to be tested.
As an alternative embodiment, the determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested includes:
determining the strain at the intersection of the reverse extension of the line elasticity phase in the stress-strain curve and the strain axis in the stress-strain curve as a rock crack closure strain;
determining the slope of the line elasticity phase of the stress-strain curve as a reference elastic modulus;
and determining the third damage variable expression according to the rock crack closing strain and the reference elastic modulus.
As an alternative embodiment, the third injury variable expression is:
D=1-σ/[E 0 (ε-ε cc )]；
wherein D is the damage variable of the rock sample to be tested, sigma is the stress of the rock sample to be tested, E 0 For the reference modulus of elasticity, ε cc For rock crack closure strain, ε is the strain of the rock sample to be tested.
In a second aspect, a computer device is provided, comprising a memory and a processor, the memory having stored thereon a computer program executable on the processor, the processor implementing the method steps according to any of the first aspects when the computer program is executed.
In a third aspect, there is provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method steps of any of the first aspects.
The application provides a method for establishing a rock theoretical damage evolution model, and the technical scheme provided by the embodiment of the application at least brings the following beneficial effects: determining a second damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain, based on the Torpedo model and the first damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain; the first damage unit number expression is constructed based on the growth rate of damage units in the rock sample to be detected along with the strain development, the growth rate of the damage units in the rock sample to be detected and the number of the damage units at the last strain moment in the rock sample to be detected; determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression; the first damage variable expression is constructed based on a number of breaking units in the rock sample to be tested and a total number of rock units in the rock sample to be tested; carrying out a uniaxial compression test on the rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, and determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested; and determining a damage variable corresponding to each strain of the rock sample to be tested according to the third damage variable expression, and performing linear fitting according to the second damage variable expression to determine a rock theoretical damage evolution model. According to the method, the stress-strain curve is obtained through a uniaxial compression experiment, and the rock damage process of the rock sample to be detected can be determined through the stress-strain curve, so that the rock damage process has the characteristics of asymmetry and the development speed is fast and slow. Therefore, based on the okay model describing the evolution process of a single species, the rock theoretical damage evolution model is determined, and the whole rock damage evolution process can be described and predicted.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for establishing a rock theoretical damage evolution model according to an embodiment of the present application;
fig. 2 is a schematic structural diagram of a rock sample to be tested according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a stress-strain curve provided in an embodiment of the present application;
fig. 4 is a schematic diagram of a damage evolution curve according to an embodiment of the present application;
FIG. 5 is a flowchart of another method for establishing a model of the evolution of theoretical damage of rock provided in an embodiment of the present application;
FIG. 6 is a schematic illustration of another stress-strain curve provided by embodiments of the present application;
FIG. 7 is a schematic diagram of stress-strain curves of three different rock samples to be tested provided in the examples of the present application;
fig. 8a is a schematic diagram of a comparison between a uniaxial compression test result of marble and a theoretical damage evolution model curve of rock according to an embodiment of the present application;
fig. 8b is a schematic diagram of a comparison between a uniaxial compression test result of red sandstone and a theoretical damage evolution model curve of rock according to an embodiment of the present application;
fig. 8c is a schematic diagram of a comparison between a uniaxial compression test result of layered siltstone and a theoretical damage evolution model curve of rock according to an embodiment of the present application;
fig. 9 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
In the following, a detailed description will be given of a method for building a theoretical damage evolution model of rock provided in the embodiment of the present application, and fig. 1 is a flowchart of a method for building a theoretical damage evolution model of rock provided in the embodiment of the present application, as shown in fig. 1, and specific steps are as follows:
and step 101, determining a second damage unit number expression of the damage units in the rock sample to be tested, which is developed along with the strain, based on the Torpedo model and the first damage unit number expression of the damage units in the rock sample to be tested, which is developed along with the strain. The first damage unit number expression is constructed based on the growth speed of the damage units in the rock sample to be tested along with the strain development, the growth rate of the damage units in the rock sample to be tested and the number of the damage units at the last strain moment in the rock sample to be tested.
In implementation, fig. 2 is a schematic structural diagram of a rock sample to be tested according to an embodiment of the present application, as shown in fig. 2. In the rock mass, the rock sample to be measured consists of a breaking unit 210 and a non-breaking unit 220. The process of breaking the rock mass sample to be measured can be regarded as a process of converting the undamaged cells 220 inside the rock mass sample to be measured into the breaking cells 210. The number of the breaking units 210 is small in the initial stage of breaking the rock mass sample to be tested, the unbroken units 220 are quickly converted to the breaking units 210, when the number of the breaking units 210 is increased to a certain degree, the increase speed of the breaking units 210 is reduced due to the restriction of the rock mass space until the increase is stopped. The okadas model is an animal population growth model that describes the rule of extinction of a single population. In the embodiment of the application, the growth rule of the damage unit 210 is compared with the species growth rule in the limited space, and the change rule of the animal population quantity along with time is equivalent to the change rule of the damage unit quantity along with the strain. Thus, a second expression of the number of breaking units that develops with strain is determined based on the Tot's model and the first expression of the number of breaking units that develops with strain in the rock sample to be tested. The first expression of the number of the breaking units is constructed based on the increasing speed of the breaking units in the rock sample to be tested along with the strain development, the increasing rate of the breaking units and the number of the breaking units at the last strain moment, and dv/dε can be used for representing the increasing speed of the breaking units along with the strain development, r (v) is used for representing the increasing rate of the breaking units, and v is used for representing the number of the breaking units at the last strain moment, namely the base number of the breaking units at the next strain moment. Where r (v) is a nonlinear reduction function of the number of destruction units v.
As an alternative embodiment, the first expression of the number of breaking units in the rock sample to be tested, which develops with strain, is:
dv/dε=r (v) v (equation one);
wherein dv/dε is the growth rate of the number of the breaking units in the rock sample to be tested along with the strain development, v is the number of the breaking units in the rock sample to be tested at the last strain moment, and r (v) is a function of the number v of the breaking units in the rock sample to be tested at the last strain moment, and represents the growth rate of the breaking units in the rock sample to be tested.
In practice, if the rock deformation development is not limited by conditions such as space environment, the growth rate of the breaking unit is proportional to the base of the previous moment, and if the ratio is r, the growth rate of the breaking unit is r, dv/dε=rv. From the embodiment of step 101, it is seen that the growth rate of the destruction units is not a constant, but a non-linear decreasing function that decreases continuously as the number of destruction units increases. Thus, the rate of increase of the breaking units in the rock sample to be tested is denoted by r (v).
As an alternative embodiment, the second expression of the number of breaking units that the breaking units develop with strain is:
dv/dε= -aln (v/k) v (formula two);
wherein dv/dε is the growth rate of the breaking units in the rock sample to be tested along with the strain development of the rock sample to be tested, a is a first model parameter, v is the number of the breaking units in the rock sample to be tested, and k is the total number of the rock units in the rock sample to be tested.
In practice, the differential formula of the okay model is: dx/dt=ax [ ln (1) -ln (x) ], where a is a parameter, which may represent the instantaneous growth rate of a species. After the okay model is introduced into the formula one (dv/dε=r (v) v), the formula one can be converted into dv/dε=av [ ln (k) -ln (v) ]= -aln (v/k) v, namely the formula two.
And 102, determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression. Wherein the first damage variable expression is constructed based on the number of breaking units in the rock sample to be tested and the total number of rock units in the rock sample to be tested.
In the implementation, the first damage variable expression is constructed based on the number of the damage units and the total number of the rock units, and the second damage variable expression of the damage variable of the rock sample to be tested, which develops along with the strain, is determined based on the second damage variable expression and the first damage variable expression;
as an alternative embodiment, the first impairment variable expression is:
d=v/k (formula three);
wherein D is a damage variable of the rock sample to be tested, v is the number of damage units in the rock sample to be tested, and k is the total number of rock units in the rock sample to be tested.
In practice, as shown in fig. 2, if the number of breaking units 210 is v and the number of unbroken units 220 is u, the total number of rock units k=v+u in the rock sample to be tested. Further assume that the area of a single broken cell 210 is equal to the area of a single unbroken cell 220, denoted as A 0 . The undamaged units are elastic bodies, satisfy Hooke's law, have equal elastic modulus and are marked as E 0 . The process of breaking the rock sample to be tested under load meets the assumption of strain equivalence. The process of converting the uncorrupted unit 220 into the corrupted unit 210 is instantaneously completed. According to the definition of the impairment variable proposed by y.n. Rabotnov, the impairment variable can be expressed as d= (v A) 0 ) /( k A 0 ) Further, a first damage variable expression d=v/k, namely a formula three, can be obtained. Wherein: v is more than or equal to 0 and less than or equal to k, so that the damage variable D E [0,1 ]]。
As an alternative embodiment, the second impairment variable expression is:
d=exp [ -exp (b-aε) ] (equation four);
wherein D is a damage variable of the rock sample to be tested, a is a first model parameter, b is a second model parameter, and epsilon is the strain of the rock sample to be tested.
In practice, substituting the first impairment variable expression (e.g., d=v/k) into the second impairment unit number expression (e.g., dv/dε= -aln (v/k) v) results in: dv/dε= kdD/dε= -aln (D) v, further, dD/dε= -aln (D) v/k= -aln (D) D, further integrating dD/dε= -aln (D) D, it can be derived: d=exp [ -exp (b-aε) ].
And 103, carrying out a uniaxial compression test on the rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, and determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested.
In the implementation, a uniaxial compression test is carried out on the rock sample to be tested, the stress value of the rock sample to be tested, which develops along with the strain, is collected, and a stress-strain curve is obtained. Fig. 3 is a schematic diagram of a stress-strain curve according to an embodiment of the present application, where, as shown in fig. 3, the abscissa is the strain of the rock sample to be tested, and the ordinate is the stress of the rock sample to be tested. Slope of line elastic phase of stress-strain curve E 0 ，E 0 And is also the reference modulus of elasticity of the rock sample to be measured. Fig. 4 is a schematic diagram of a damage evolution curve provided in the embodiment of the present application, as shown in fig. 4, in which a rock sample to be tested is a natural rock containing microcracks and pores with different dimensions, and has initial damage, and the stress-strain curve of the rock in the whole process of uniaxial compression deformation damage can be divided into 5 stages of primary initial defect recovery, damage-free retention, damage start, damage acceleration and damage alleviation, which are sequentially stage I, stage II, stage III, stage IV and stage V in fig. 3 and fig. 4. The initial damage in the rock sample to be tested is closed by compaction (stage I) at the initial stage of the load application of the uniaxial compression test, the damage degree gradually approaches to 0, then the rock sample to be tested enters a linear elastic deformation stage (stage II), the initial damage in the rock is completely closed by compression, almost no new cracks are generated, and the rock sample to be tested approaches to a complete nondestructive state or a state with the minimum damage degree and is kept for a period of time. Therefore, if the initial nonlinear deformation of the rock is not considered, the stress-strain curve can be transformed from the stage II to the third damage variable expression can be obtained assuming that the rock sample to be tested is loaded directly into the linear elastic deformation stage.
Fig. 5 is a flowchart of another method for establishing a model of the theoretical damage evolution of rock according to an embodiment of the present application. As shown in fig. 5, in step 103, according to the stress-strain curve of the rock sample to be tested, the specific steps for determining the third damage variable expression are as follows:
step 501, determining the strain at the intersection of the reverse extension of the line elasticity phase in the stress-strain curve and the strain axis in the stress-strain curve as the rock crack closure strain.
In practice, fig. 6 is a schematic diagram of another stress-strain curve provided in an embodiment of the present application, as shown in fig. 6. Assuming that the rock sample to be tested directly enters a linear elastic deformation stage (stage II in the figure) when being loaded, the stress axis of the stress-strain curve obtained by the testσMove to the intersection point of the strain axis after the linear elastic stage is reversely prolongedO'I.e. stress axis in the figureσ'Is a position of (c). Stress axisσ'Intersection point of reverse extension line of elastic phase of line on strain axis epsilonO'The crack closure strain point is obtained. Closing the crack to the strain pointO'The corresponding strain on the strain axis epsilon is determined as rock crack closure strain epsilon cc 。
Step 502, determining the slope of the line elasticity phase in the stress-strain curve as the reference elastic modulus.
In practice, the slope of the line elastic phase in the stress-strain curve is determined as the reference elastic modulus E 0 。
A third damage variable expression is determined based on the rock crack closure strain and the reference elastic modulus, step 503.
In practice, a third damage variable expression may be determined from the rock crack closure strain and the reference elastic modulus.
As an alternative embodiment, the third impairment variable expression in step 503 is:
D=1-σ/[E 0 (ε-ε cc )](equation five);
wherein D is the damage variable of the rock sample to be tested, sigma is the stress of the rock sample to be tested, E 0 For the reference modulus of elasticity, ε cc For rock crack closure strain, ε is the strain of the rock sample to be tested.
In practice, degradation of material properties due to crack growth in rock material can be used as an indicator of the extent of rock damage, based on continuityThe relationship between the material damage variable D and the effective modulus of the medium damage mechanics is as follows: d=1-E/E 0 =1-(σ/ε)/ E 0 . Wherein E and E 0 The elastic moduli of the damaged and undamaged materials are shown, respectively. Stress epsilon based on rock crack closure cc And a reference elastic modulus E 0 A third impairment variable expression may be determined: d=1- [ σ/(ε - ε) cc )]/ E 0 =1-σ/[E 0 (ε-ε cc )]。
And 104, determining a damage variable corresponding to each strain of the rock sample to be tested according to the third damage variable expression, and performing linear fitting according to the second damage variable expression to determine a rock theoretical damage evolution model.
In implementation, according to a formula five, the damage variable D of each rock sample to be tested under each strain epsilon condition in the uniaxial compression test process can be calculated. Several sets of data will be obtained, such as: (epsilon) 1 ，D 1 ）、（ε 2 ，D 2 ）、（ε 3 ，D 3 ）、（ε 4 ，D 4 ）…（ε n ，D n ) And performing linear fitting according to a formula IV to determine a first model parameter a and a second model parameter b in the formula IV. After the first model parameter a and the second model parameter b are determined, a rock theoretical damage evolution model D=exp < -exp (b-aε) can be obtained]。
As an alternative implementation, fig. 7 is a schematic diagram of stress-strain curves of three different rock samples to be tested provided in the example of the present application, as shown in fig. 7, specifically as follows:
and processing three different types of rock samples to be tested, namely marble, red sandstone and lamellar siltstone, which are collected from an engineering site, into a standard cylinder sample with the height of 100mm and the diameter of 50 mm. And then carrying out indoor uniaxial compression test on the three types of rock samples to be tested to obtain stress-strain curves of the three types of rock samples to be tested. Wherein, the dashed curve in fig. 7 represents marble, the thin solid curve represents red sandstone, the thick solid curve represents layered siltstone, the abscissa is strain, and the ordinate is stress. According to the dotted curve in the figure (marble)The intersection point of the reverse extension line of the line elastic stage and the transverse axis can determine that the rock crack closure strain corresponding to marble is 0.07% and the reference elastic modulus is 28.97GPa. Similarly, the rock crack closure strain of red sandstone (thin solid curve) was 0.10%, the reference elastic modulus was 15.20GPa, and the rock crack closure strain of layered siltstone (thick solid curve) was 0.18%, the reference elastic modulus was 11.00GPa. Substituting the above data into d=1- σ/[ E ] 0 (ε-ε cc )]The following three formulas are available:
marble: d (D) d =1-σ/[28.97(ε-0.07)]；
Red sandstone: d (D) h =1-σ/[15.2(ε-0.1)]；
Layered silty sandstone: d (D) c =1-σ/[11(ε-0.18)]。
The damage variable corresponding to each strain epsilon of each rock sample to be tested in the uniaxial compression test process can be calculated through the three formulas. Taking marble as an example: fitting the calculation results according to the rock theory damage evolution model d=exp [ -exp (b-aε) ] can obtain b=8.0229, a=17.07. Thus, the rock theory damage evolution model d=exp [ -exp (8.0229-17.07 epsilon) ].
Similarly, the rock theoretical damage evolution model of the red sandstone is D=exp < -exp (11.072-17.30 epsilon) ], and the rock theoretical damage evolution model of the layered siltstone is D=exp < -exp (10.656-13.32 epsilon) ].
In order to verify the rationality of the rock theoretical damage evolution model, the uniaxial compression test results of marble, red sandstone and lamellar siltstone are compared with the rock theoretical damage evolution model curve. Fig. 8a is a schematic diagram of a comparison between a uniaxial compression test damage result and a rock theoretical damage evolution model curve, which are provided by the embodiment of the present application, in which marble is taken as an example, fig. 8b is a schematic diagram of a comparison between a uniaxial compression test damage result and a rock theoretical damage evolution model curve, which are provided by the embodiment of the present application, in which red sandstone is taken as an example, fig. 8c is a schematic diagram of a comparison between a uniaxial compression test damage result and a rock theoretical damage evolution model curve, which are provided by the embodiment of the present application, in which layered siltstone is taken as an example, as shown in fig. 8a, fig. 8b and fig. 8c, the abscissa is the strain, and the ordinate is the damage variable. Taking fig. 8a as an example, the short dashed line in fig. 8a is a theoretical damage evolution model curve of rock provided in the embodiment of the present application, and the black solid circle curve is a uniaxial compression test result (such as a stress-strain curve) of marble. It can be seen that in the compression deformation process of the rock sample (marble) to be tested, the damage variable undergoes 5 stages of damage-free maintenance, damage start, damage acceleration, damage change alleviation and complete damage, the whole is in an S-shaped development trend, the rock theoretical damage evolution model curve obtained based on the Gangbo model fitting has high fitting degree with test results, and the rock theoretical damage evolution model curve of red sandstone and lamellar siltstone has high fitting degree with test results. This shows that the rock theoretical damage evolution model established based on the okay model can well describe the rock deformation damage variable evolution process.
The embodiment of the application provides a method for establishing a rock theoretical damage evolution model, and the technical scheme provided by the embodiment of the application at least brings the following beneficial effects: determining a second damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain, based on the Torpedo model and the first damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain; the first damage unit number expression is constructed based on the growth rate of the damage units in the rock sample to be tested along with the strain development, the growth rate of the damage units in the rock sample to be tested and the number of the damage units at the last strain moment in the rock sample to be tested; determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression; the first damage variable expression is constructed based on the number of damage units in the rock sample to be tested and the total number of rock units in the rock sample to be tested; carrying out a uniaxial compression test on the rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, and determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested; and determining a damage variable corresponding to each strain of the rock sample to be tested according to the third damage variable expression, and performing linear fitting according to the second damage variable expression to determine a rock theoretical damage evolution model. According to the method, the stress-strain curve is obtained through a uniaxial compression experiment, and the rock damage process of the rock sample to be detected can be determined through the stress-strain curve, so that the rock damage process has the characteristics of asymmetry and the development speed is fast and slow. Therefore, based on the okay model describing the evolution process of a single species, the rock theoretical damage evolution model is determined, and the whole rock damage evolution process can be described and predicted.
It should be understood that, although the steps in the flowcharts of fig. 1 and 5 are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least a portion of the steps in fig. 1 and 5 may include a plurality of steps or stages, which are not necessarily performed at the same time, but may be performed at different times, and the order of the execution of the steps or stages is not necessarily sequential, but may be performed in turn or alternately with at least a portion of the steps or stages in other steps or other steps.
It should be understood that the same/similar parts of the embodiments of the method described above in this specification may be referred to each other, and each embodiment focuses on differences from other embodiments, and references to descriptions of other method embodiments are only needed.
In one embodiment, a computer device is provided, as shown in fig. 9, including a memory and a processor, where the memory stores a computer program that can be executed on the processor, and the processor executes the method steps for building a theoretical damage evolution model of rock.
In one embodiment, a computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of the method of modeling rock theoretical damage evolution described above.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
It should be noted that, user information (including but not limited to user equipment information, user personal information, etc.) and data (including but not limited to data for presentation, analyzed data, etc.) referred to in the present application are information and data authorized by the user or sufficiently authorized by each party.
In this specification, each embodiment is described in a related manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
Claims (7)
1. A method of modeling the evolution of theoretical damage to rock, the method comprising:
determining a second damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain, based on the Torpedo model and the first damage unit number expression of the damage units in the rock sample to be tested, which develops along with the strain; the first damage unit number expression is constructed based on the growth rate of damage units in the rock sample to be detected along with the strain development, the growth rate of the damage units in the rock sample to be detected and the number of the damage units at the last strain moment in the rock sample to be detected;
determining a second damage variable expression of the damage variable of the rock sample to be tested according to the strain development based on the second damage unit number expression and the first damage variable expression; the first damage variable expression is constructed based on a number of breaking units in the rock sample to be tested and a total number of rock units in the rock sample to be tested;
carrying out a uniaxial compression test on the rock sample to be tested, obtaining a stress-strain curve of the rock sample to be tested, and determining a third damage variable expression according to the stress-strain curve of the rock sample to be tested;
and determining a damage variable corresponding to each strain of the rock sample to be tested according to the third damage variable expression, and performing linear fitting according to the second damage variable expression to determine a rock theoretical damage evolution model.
2. The method of claim 1, wherein the first expression of the number of breaking units in the rock sample to be tested that develops with strain is:
dv/dε=r(v)v；
wherein dv/dε is the growth rate of the number of the breaking units in the rock sample to be tested along with the strain development, v is the number of the breaking units in the rock sample to be tested at the last strain moment, and r (v) is a function of the number v of the breaking units in the rock sample to be tested at the last strain moment, and represents the growth rate of the breaking units in the rock sample to be tested.
3. The method of claim 1, wherein the number of breaking units in the rock sample to be tested that develop with strain is expressed as:
dv/dε=-aln(v/k)v；
wherein dv/dε is the growth rate of the breaking units in the rock sample to be tested along with the strain development of the rock sample to be tested, a is a first model parameter, v is the number of the breaking units in the rock sample to be tested, and k is the total number of the rock units in the rock sample to be tested.
4. The method of claim 1, wherein the first impairment variable expression is:
D=v/k；
wherein D is a damage variable of the rock sample to be tested, v is the number of damage units in the rock sample to be tested, and k is the total number of rock units in the rock sample to be tested.
5. The method of claim 1, wherein the second impairment variable expression is:
D=exp[-exp(b-aε)]；
wherein D is a damage variable of the rock sample to be tested, a is a first model parameter, b is a second model parameter, and epsilon is the strain of the rock sample to be tested.
6. The method of claim 1, wherein determining a third impairment variable expression from the stress-strain curve of the rock sample to be tested comprises:
determining the strain at the intersection of the reverse extension of the line elasticity phase in the stress-strain curve and the strain axis in the stress-strain curve as a rock crack closure strain;
determining the slope of the line elasticity phase of the stress-strain curve as a reference elastic modulus;
and determining the third damage variable expression according to the rock crack closing strain and the reference elastic modulus.
7. The method of claim 6, wherein the third impairment variable expression is:
D=1-σ/[E 0 (ε-ε cc )]；
wherein D is the damage variable of the rock sample to be tested, sigma is the stress of the rock sample to be tested, E 0 For the reference modulus of elasticity, ε cc For rock crack closure strain, ε is the strain of the rock sample to be tested.
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