Method for constructing constitutive equation of mudstone damage based on acoustic emission and resistivity parameters

Abstract

The application discloses a method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, which comprises the following steps: S1, uniaxial cyclic loading and unloading is carried out on a mudstone sample; S2, the damage process of the mudstone in the loading stage is represented by taking acoustic emission ringing count as a damage variable; S3, the damage process of the mudstone in the unloading stage is represented by taking resistivity as a damage variable; and S4, the damage constitutive equation of the mudstone under the uniaxial cyclic loading and unloading is established by correcting the strength of the mudstone according to the water content. The corrected damage variable of the application is based on the two physical quantities of acoustic emission ringing count and resistivity, and the development of rock cracks under the loading and unloading states is represented from the two angles of the generation of new cracks and the penetration of original cracks, so that the damage deformation of the rock under the uniaxial cyclic loading and unloading stress state can be accurately and truly described compared with a single physical quantity.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of rock analysis, in particular to a mudstone damage constitutive equation construction method based on acoustic emission and resistivity parameters. BACKGROUND

[0002] It is inaccurate to judge the damage of rock under loading and unloading states and the development of rock cracks by relying on a single physical quantity, and the judgment result has errors and cannot well reflect the real situation of rock internal damage. Acoustic emission ring count mainly occurs in the loading stage. Based on Kaiser principle, when the residual stress does not exceed the previous unloading limit, acoustic emission ring count rarely occurs when reloading. It is indicated that acoustic emission ring count rarely occurs in the unloading stage after the single peak limit load. Therefore, it is not suitable to use acoustic emission ring count as a damage variable to characterize the damage state of rock in the unloading stage. Meanwhile, in the loading state, the crack spacing of rock is reduced, the current channel is weakened, and the resistivity change is slowed down. There is an obvious error in using resistivity to characterize the damage state in the loading stage mainly for crack initiation. Meanwhile, the damage variable defined by resistivity has the problem that the plastic strain of mudstone is large and the resistivity change is small in the initial low stress compaction stage, and the damage variable defined by resistivity has the problem that the damage is small due to less resistivity receiving signal in the early stage. Therefore, a damage constitutive equation capable of accurately and truly describing the damage deformation of rock under the uniaxial cyclic loading and unloading stress state is needed. SUMMARY

[0003] In order to solve the above problems, the application provides a mudstone damage constitutive equation construction method based on acoustic emission and resistivity parameters and a construction method, and the technical scheme is as follows:

[0004] The application provides a mudstone damage constitutive equation construction method based on acoustic emission and resistivity parameters, which comprises the following steps: S1, uniaxial cyclic loading and unloading is performed on a mudstone sample; S2, acoustic emission ring count is used as a damage variable to represent the damage process of mudstone in the loading stage; S3, resistivity is used as a damage variable to represent the damage process of mudstone in the unloading stage; and S4, the strength of mudstone is corrected according to the water content, and a damage constitutive equation of mudstone under the action of uniaxial cyclic loading and unloading is established.

[0005] For example, in the mudstone damage constitutive equation construction method based on acoustic emission and resistivity parameters provided in an embodiment, in S2, the loading stage acoustic emission parameter loss variable D S is defined based on the cumulative ring count:

[0006]

[0007] wherein σ c is the residual stress, and σmax peak stress, M f cumulative acoustic emission ring-down count, M N cumulative acoustic emission ring-down count at complete failure of the mudstone.

[0008] For example, in an embodiment of the method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, in S3, the unloading stage resistivity parameter damage variable D is defined based on resistivity ρ is:

[0009]

[0010] wherein p is the resistivity of the mudstone at the time of testing, and p0 is the resistivity of the mudstone in an undamaged state.

[0011] For example, in an embodiment of the method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, in S3, the plastic strain is introduced in the unloading stage to correct the resistivity parameter damage variable.

[0012] For example, in an embodiment of the method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, in S4, the elastic modulus correction coefficient a based on the water content W quantitatively characterizes the relationship between the water content of the mudstone and the strength of the mudstone, a W satisfies the following relationship:

[0013]

[0014] wherein E0 is the elastic modulus of the dry mudstone in the cyclic loading and unloading process, E W is the elastic modulus of the mudstone with different water contents in the cyclic loading and unloading process, E W satisfies the following relationship:

[0015] E W = -8.95W 3 + 26.15W 2 - 20.40W + 18.09

[0016] wherein W is the water content of the mudstone.

[0017] For example, in an embodiment of the method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, the damage constitutive equation of the mudstone under uniaxial cyclic loading and unloading stress state is:

[0018]

[0019] wherein s L is the stress in the loading stage, s U is the stress in the unloading stage, and e is the strain.j cumulative plastic strain, εp, for the peak stress of the last cycle p cumulative plastic strain, εp, for the peak stress of the last cycle.

[0020] The method provided by some embodiments of the present application has the beneficial effects that the damage constitutive equation is used to describe the damage state of the rock under the cyclic loading and unloading, the damage process of the elastic modulus of the mudstone in the loading and unloading process is reflected from the perspective of the crack penetration and development under the load based on the resistivity and acoustic emission signals, the stress-strain curve of the mudstone under the loading state can be accurately fitted by the damage constitutive equation based on the acoustic emission ringing count, the resistivity damage variable under the unloading state is corrected by introducing the plastic strain, and the problem that the damage is less due to less received signals of the resistivity at the early stage is effectively solved by the corrected damage variable based on the plastic strain accumulation, so that the overall damage change trend is closer to the real damage of the rock.

[0021] The present application considers the influence of different water contents on the strength of the mudstone, the corrected damage variable is based on the acoustic emission ringing count and the resistivity, and the development of the cracks of the rock under the loading and unloading states is characterized from the perspectives of the generation of new cracks and the penetration of original cracks, so that the damage deformation of the rock under the uniaxial cyclic loading and unloading stress state can be accurately and truly described compared with a single physical quantity. BRIEF DESCRIPTION OF DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0023] Figure 1 is a method flowchart of the present application;

[0024] Figure 2 is a relationship diagram of the acoustic emission defined damage variable-strain during the loading and unloading process of the mudstone sample;

[0025] Figure 3 is a relationship diagram of the resistivity defined damage variable-strain during the loading and unloading process of the mudstone sample;

[0026] Figure 4 is a comparison difference diagram of the resistivity and acoustic emission defined damage;

[0027] Figure 5 is a fitting curve diagram of the loading stage damage constitutive equation;

[0028] Figure 6 is the uncorrected damage constitutive equation fitting the unloading stage curve;

[0029] Figure 7 is the corrected damage constitutive equation fitting the unloading stage curve;

[0030] Figure 8 is the first cycle fitting curve of the mudstone sample;

[0031] Figure 9 is the second cycle fitting curve of the mudstone sample;

[0032] Figure 10 is the third cycle fitting curve of the mudstone sample;

[0033] Figure 11 is the fourth cycle fitting curve of the mudstone sample;

[0034] Figure 12 is the fifth cycle fitting curve of the mudstone sample;

[0035] Figure 13 is the sixth cycle fitting curve of the mudstone sample;

[0036] Figure 14 is the seventh cycle fitting curve of the mudstone sample. DETAILED DESCRIPTION

[0037] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0038] Unless otherwise defined, the technical terms or scientific terms used in the present disclosure should be understood as the common meanings thereof by those skilled in the art to which the present disclosure belongs. The terms "first", "second", and similar terms used in the present disclosure do not indicate any order, quantity, or importance, but are used to distinguish different components. The terms "include", "contain", and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "upper", "lower", "left", "right", and the like are only used to indicate relative positional relationships, and when the absolute positions of the described objects change, the relative positional relationships may also change accordingly.

[0039] The application provides a method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters, which comprises the following steps as shown in the figure: Figure 1

[0040] S1: uniaxial cyclic loading and unloading is performed on a mudstone sample;

[0041] S2: the acoustic emission ring count is used as a damage variable to represent the damage process of the mudstone in the loading stage;

[0042] S3: the resistivity is used as a damage variable to represent the damage process of the mudstone in the unloading stage;

[0043] S4: the strength of the mudstone is corrected according to the water content, and a damage constitutive equation of the mudstone under uniaxial cyclic loading and unloading is established.

[0044] The method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters considers the influence of different water contents on the strength of the mudstone, simultaneously uses the resistivity and acoustic emission signals to judge the development state of internal cracks of the rock under the action of the load, and represents the damage state of the rock, and establishes a damage constitutive equation of the mudstone under uniaxial cyclic loading and unloading.

[0045] In order to construct the damage constitutive equation, the influence of water on the strength of the rock needs to be considered first. When there is a large amount of pore water in the rock, the friction between mineral crystals will be weakened, especially when there are a large number of clay minerals in the rock, the rock will soften and deform after absorbing water, and a weak interlayer will be formed inside, which will accelerate the reduction of the overall strength of the rock. The water content will weaken the elastic modulus of the rock, so the water content, as an important factor affecting the strength of the rock, needs to be corrected based on the water content first. The relationship curve between different water contents and the elastic modulus of the mudstone is fitted to obtain the fitting equation (the fitting goodness coefficient R 2 is 0.962):

[0046] E W = -8.95W 3 + 26.15W 2 - 20.40W + 18.09

[0047] Wherein, W is the water content of the mudstone, and E W is the elastic modulus of the mudstone with different water contents in the process of cyclic loading and unloading.

[0048] Based on the above relationship equation, an elastic modulus correction coefficient a W based on the water content is proposed to quantitatively represent the relationship between the water content of the rock and the strength of the mudstone:

[0049]

[0050] ​E0 is the elastic modulus of dry mudstone in the cyclic loading and unloading process.

[0051] Elastic modulus and correction coefficient a of mudstone with different water contents W As shown in Table 1:

[0052] Table 1 Elastic modulus of mudstone with different water contents

[0053]

[0054] For example, in the method for constructing a mudstone damage constitutive equation based on acoustic emission and resistivity parameters provided in an embodiment, the damage constitutive equation of mudstone under uniaxial cyclic loading and unloading stress state is:

[0055]

[0056] wherein σ L is the stress in the loading stage, σ U is the stress in the unloading stage, v is the strain, ε j is the cumulative plastic strain of the peak stress in a single cycle, ε p is the cumulative plastic strain of the peak stress in the last cycle, D S is the acoustic emission parameter loss variable in the loading stage, D ρ is the resistivity parameter loss variable in the unloading stage.

[0057] Under the action of cyclic load, mudstone generates micro-pores and cracks in the interior and is accompanied by energy release, and internal damage gradually accumulates, eventually leading to overall failure of the rock. As an important non-destructive testing technology, acoustic emission technology can accurately detect the damage state of the rock. Acoustic emission count and cumulative count, as important parameters of acoustic emission testing, can better reflect the damage state of the rock in the compression process. In order to facilitate the description of the damage state of mudstone based on the damage variable defined by the acoustic emission parameter, it is assumed that when the mudstone is undamaged, the damage variable is 0, but due to the insufficient strength of the test rig and the test mechanism, the specimen is stopped from being pressed when the peak stress is reached before it is completely destroyed, that is, the damage variable cannot completely reach 1.0. Therefore, the peak stress and residual stress are used to correct the damage variable, and the acoustic emission parameter loss variable D S in the loading stage defined based on the cumulative ring count is:

[0058]

[0059] wherein σ c is the residual stress, σ max is the peak stress, M f is the cumulative ring count of acoustic emission, M N is the cumulative ring count of acoustic emission when the mudstone is completely destroyed.

[0060] Due to the too fast strain rate of the last cycle unloading stage, the data statistics are incomplete. Therefore, the strain data of loading and unloading in the last second cycle and the corresponding cumulative ringing count damage factor are analyzed. According to the Boltzmann equation, the relationship between the acoustic emission and strain damage of the four samples in the last second cycle is fitted as follows: Figure 2 It can be seen from the acoustic emission defined damage variable-strain relationship diagram of the mudstone sample in the loading and unloading process that the damage increases rapidly in the early loading stage, and remains basically unchanged in the unloading stage. Based on the Kaiser principle, under the action of load in the loading stage, the original cracks of the rock close, and new cracks initiate, thereby releasing a large amount of energy. In the unloading stage after reaching the peak stress, the elastic part of the rock recovers, the overall strain decreases, the original cracks re-open, and the original cracks gradually connect with each other, while the crack aperture expands, and basically no new crack initiates. The energy released by the mutual connection of the original cracks is far less than the energy released by the initiation of new cracks. Therefore, in the loading stage, the acoustic emission ringing count is more, and the damage variable grows faster, while in the unloading stage, the acoustic emission count is less, and the damage basically remains unchanged. In summary, the acoustic emission defined damage variable reflects the rock damage in the loading stage more accurately, and the acoustic emission ringing count as the damage variable is more suitable for characterizing the damage process of the mudstone in the loading stage.

[0061] The acoustic emission-strain damage relationship of the last second cycle of the four samples is fitted according to the Boltzmann equation as follows, and it is found that good fitting (R 2 >0.91) is achieved, and the results of the parameters are shown in Table 2:

[0062] D s =A2+(A1-A2) / (1+exp(ε-A3 / A4))

[0063] Table 2 Fitting parameters of acoustic emission damage-strain of mudstone

[0064]

[0065] During the cyclic stress action, the rock cracks will continuously develop due to the load action, the internal damage will continuously accumulate, and eventually a large number of through cracks will be formed to cause overall damage. Since the resistivity is sensitive to the development of cracks, the expansion of cracks to form water flow channels can greatly reduce the rock resistivity, so the development of rock cracks can be directly reflected by the resistivity, and the rock damage state is characterized. In order to quantitatively characterize the relationship between the rock resistivity and the damage state, based on the damage theory, the unloading stage resistivity parameter loss variable D ρ is proposed based on the definition of resistivity:

[0066]

[0067] where p is the resistivity of the mudstone at the time of testing, and p0 is the resistivity of the mudstone in the undamaged state. Resistivity is a function related to strain. At the beginning, the pressure is small, and the rock is undamaged, i.e., the damage is 0. With the action of the load, the resistivity decreases, and the rock damage gradually increases. Since the resistivity is a basic physical index of the rock, even at the time of complete destruction, the resistivity still exists, and therefore, the damage variable cannot be 1.0.

[0068] The relationship between the strain and the resistivity damage of the mudstone sample in the last second loading cycle is shown in FIG. 4. Figure 3 The initiation of the crack during loading leads to a gradual increase in damage, and with the increase in the load, the damage also increases synchronously. During unloading, the elastic part rebounds, the crack channel expands, the resistivity changes rapidly, and the rock damage increases. Compared with the loading stage, the damage in the unloading stage is mainly caused by the connection and expansion of the crack, and therefore, the resistivity changes more rapidly in the unloading stage, and the reflection of the rock damage is more sensitive and accurate. Therefore, the resistivity is more suitable for representing the damage process of the mudstone in the unloading stage.

[0069] Since the plastic strain of the mudstone accumulates relatively more during the last second cycle, the damage changes greatly, and therefore, the damage variable-strain relationship curve of the last second cycle of different samples is fitted by using a cubic polynomial equation. The results show that the fitting effect is good (R 2 > 0.95, see Table 3), and therefore, the damage variable equation can be established according to the fitting parameters.

[0070] D ρ = A e 3 +B e 2 +C e + D

[0071] Table 3 Fitting parameters of the resistivity damage-strain of the mudstone

[0072]

[0073]

[0074] Figure 4 The comparison difference diagram of the resistivity and acoustic emission defined damage is shown in FIG. 5, and according to the results, the resistivity damage is more sensitive and accurate than the acoustic emission damage. Figure 4Based on the test results, the damage variable fitting curves of acoustic emission and resistivity are obviously different, and a single physical quantity cannot accurately reflect the damage state of rock. Although both resistivity and acoustic emission can reflect the crack condition of rock, the angles of reflection are different. Resistivity is related to crack channels, and the formation and expansion of connected cracks have a greater impact on the change of resistivity. During unloading, the elastic rebound of rock leads to crack expansion and connection, and the change of resistivity is obvious, so resistivity is more suitable for describing the damage process in the unloading stage. The ring count of acoustic emission essentially reflects the number of crack generation, which mainly occurs in the loading process and rarely occurs in the unloading stage. Therefore, the ring count of acoustic emission is suitable for reflecting the rock damage in the loading stage. Therefore, acoustic emission and resistivity are considered to be used together to reflect the change of rock cracks.

[0075] As Figure 5 shown, in the loading stage, the damage constitutive equation based on the cumulative ring count of acoustic emission can accurately fit the stress-strain curve of mudstone.

[0076] Mudstone is a standard elastic-plastic body, and will simultaneously occur elastic and plastic deformation under load. As Figures 6-7 shown, in the unloading stage, the elastic deformation will gradually recover, while the plastic strain will continue to accumulate. Especially when the unloading stress is below 20 MPa, the elastic part of the mudstone will quickly rebound, the plastic strain will decrease, and the overall strain change will accelerate. While the load is in the unloading stage of 20-60 MPa, the slope of the damage fitting curve is basically consistent with the test curve. At the same time, as Figure 6 shown, because in the initial low stress compaction stage, the plastic strain of mudstone is large and the change of resistivity is small, it is necessary to introduce the plastic strain to modify the resistivity damage variable in the unloading state. The fitting curve of the damage constitutive equation after modification is as Figure 7 shown, based on the plastic strain accumulation modified damage variable, the problem of less damage caused by less received signal of resistivity in the early stage is effectively solved, and the plastic strain is introduced to modify the resistivity damage variable to solve Figure 6 the problem of too fast deformation in the unloading stage under low stress, so that the overall damage change trend is closer to the real damage of rock.

[0077] The accuracy test of the mudstone damage constitutive equation based on acoustic emission and resistivity parameters in the present application: from Figures 8-14The 7-cycle test and fitting results of the shown mudstone sample show that, except for the first unloading process, the variance of the fitting curve is less than 95%, the equation of the remaining fitting curve is greater than 95%, and the reliability of the fitting curve is high. There are some fitting flaws in a small range near the peak stress, but the maximum stress difference is basically less than 3MPa. Since the peak stress obtained by the fitting curve during the loading process is basically consistent with the actual peak stress, the peak stress can be determined. At the same time, the stress difference between the fitting curve and the actual curve is less than 2MPa, and the overall relative error is less than 5%, and the fitting effect is good. Therefore, the damage constitutive equation can accurately describe the stress-strain condition of mudstone in the process of cyclic loading and unloading.

[0078] The damage constitutive equation constructed by the acoustic emission ringing count and the damage variable defined by resistivity is used in the present application, and the stress-strain curve of the mudstone in the process of uniaxial cyclic loading and unloading is fitted using the modified damage constitutive equation. The fitting curve of different samples is consistent with the actual curve, and the modified damage variable in the present application is based on the acoustic emission ringing count and the resistivity, which respectively characterizes the development of rock cracks under loading and unloading from the perspectives of the generation of new cracks and the penetration of original cracks. Compared with a single physical quantity, it can accurately and truly describe the damage deformation of rock under uniaxial cyclic loading and unloading stress state.

[0079] Although the embodiments of the present application have been disclosed as above, they are not limited to the use listed in the specification and embodiments, and can be fully applied to various fields suitable for the present application. For those skilled in the art, other modifications can be easily realized, and therefore the present application is not limited to specific details and examples shown and described herein, without departing from the general concept defined by the claims and equivalent scope.

Claims

1. A method for constructing constitutive equations for mudstone damage based on acoustic emission and resistivity parameters, characterized in that, Includes the following steps: S1 performs uniaxial cyclic loading and unloading on the mudstone sample; S2 uses acoustic emission ringing count as a damage variable to characterize the damage process of mudstone during the loading stage; S3 uses resistivity as a damage variable to characterize the damage process of mudstone during the unloading stage. S4 corrects the mudstone strength based on the water content and establishes the damage constitutive equation of mudstone under uniaxial cyclic loading and unloading. In S4, the elastic modulus correction coefficient α based on moisture content W Quantitative characterization of the relationship between mudstone water content and mudstone strength, α W The following relationship must be satisfied: ； Where E0 is the elastic modulus of the dry mudstone during the cyclic loading and unloading process, E W E represents the elastic modulus of mudstone with different water contents during cyclic loading and unloading processes. W The following relationship must be satisfied: ； Where W represents the water content of the mudstone; The damage constitutive equation for mudstone under uniaxial cyclic loading and unloading stress is: ； Where, σ L For the stress during the loading stage, σ U ε represents the stress during the unloading stage, and ε represents the strain. j ε is the cumulative plastic strain of the peak stress in a single cycle. p D is the cumulative plastic strain of the peak stress in the last cycle. S D represents the loss variable of acoustic emission parameters during the loading phase. ρ The resistivity parameter loss variable during the unloading phase.

2. The method for constructing the constitutive equation for mudstone damage based on acoustic emission and resistivity parameters according to claim 1, characterized in that, In S2, the acoustic emission parameter loss variable D during the loading stage is defined based on the cumulative ringing count. S for: ； Where, σ c For residual stress, σ max For peak stress, M f M is the cumulative ring count for acoustic emissions. N The cumulative ringing count of acoustic emissions when the mudstone is completely destroyed.

3. The method for constructing the constitutive equation of mudstone damage based on acoustic emission and resistivity parameters according to claim 2, characterized in that, In S3, the resistivity parameter loss variable D during the unloading phase is based on the resistivity definition. ρ for: ； Where ρ is the resistivity of mudstone during the test, and ρ0 is the resistivity of mudstone in its undamaged state.

4. The method for constructing the constitutive equation for mudstone damage based on acoustic emission and resistivity parameters according to claim 3, characterized in that, In step S3, plastic strain is introduced during the unloading phase to correct the damage variable of the resistivity parameter.

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