Method, device, medium and equipment for analyzing deformation of surrounding rock of underground lining gas storage of compressed air energy storage power station

Abstract

The application discloses a compressed air energy storage power station underground lining gas storage reservoir surrounding rock deformation analysis method, device, medium and equipment, and belongs to the technical field of surrounding rock deformation analysis. The method comprises the following steps: constructing a compressed air energy storage power station underground lining gas storage reservoir surrounding rock deformation analysis model; obtaining characteristic parameters of the compressed air energy storage power station underground lining gas storage reservoir surrounding rock to be analyzed; inputting the characteristic parameters into the model; and obtaining the deformation conclusion of the compressed air energy storage power station underground lining gas storage reservoir surrounding rock to be analyzed through operation of the compressed air energy storage power station underground lining gas storage reservoir surrounding rock deformation analysis model. The device, medium and equipment can be used to realize the method. The gas storage reservoir surrounding rock deformation analysis model and the implementation method based on the fractal order derivative theory can accurately describe the fatigue damage evolution law of the surrounding rock under the long-term high pressure and large amplitude internal pressure working condition, and the constitutive equation under the triaxial cyclic load is derived.

Description

Technical Field

[0001] This invention relates to the field of surrounding rock deformation analysis technology, and in particular to a method, apparatus, medium and equipment for analyzing the surrounding rock deformation of an underground lining gas storage tank in a compressed air energy storage power station. Background Technology

[0002] As the global energy structure transitions towards low-carbon development, compressed air energy storage (CAES) has become a key technology for ensuring the stable operation of new power systems due to its large-scale and low-cost advantages. While artificially lined chambers, as the core energy storage carrier of CAES power plants, offer advantages such as flexible site selection and significant economies of scale, their surrounding rock must continuously withstand high pressure and large amplitude cyclic internal pressure during long-term operation. This periodic loading and unloading leads to the continuous initiation, propagation, and penetration of microcracks within the surrounding rock, thereby threatening the structural stability of the gas storage facility. Therefore, establishing a constitutive model that accurately characterizes the deformation patterns and damage evolution characteristics of the surrounding rock of artificially lined chambers under cyclic loading is a core issue in evaluating the life-cycle stability of the surrounding rock.

[0003] Existing technologies suffer from low computational efficiency when analyzing the long-term fatigue process of compressed air energy storage power station chambers. In contrast, fractal derivatives, as a local operator, do not involve convolution calculations and can significantly improve computational efficiency while maintaining accuracy. Current research on fractal constitutive models mainly focuses on the creep characteristics of rocks, and research on constitutive models under cyclic loading is still insufficient. Summary of the Invention

[0004] In view of this, the present invention provides a method, device, medium and equipment for analyzing the deformation of the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. It is based on the fractal derivative theory of the deformation analysis model and implementation method of the surrounding rock of the gas storage tank, and derives its constitutive equation under triaxial cyclic loading. It aims to accurately describe the fatigue damage evolution law of the surrounding rock under long-term high pressure and large amplitude internal pressure conditions, thus making it more suitable for practical use.

[0005] To achieve the first objective mentioned above, the technical solution of the method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station provided by this invention is as follows: The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station provided by this invention includes the following steps: Construct a deformation analysis model for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station; Obtain characteristic parameters of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station to be analyzed; The characteristic parameters of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed are input into the deformation analysis model of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station. After calculation, the deformation conclusion of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed is obtained.

[0006] The deformation analysis of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station provided by the present invention can also be further achieved by the following technical measures.

[0007] Preferably, the construction of the deformation analysis model for the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station specifically includes the following steps: Step S1: For the viscoelastic response of rock under cyclic loading, a fractal viscous element is defined based on the fractal derivative theory, and a linear mapping relationship between stress and strain fractal derivatives is established. The nonlinear characteristics of rock rheology are characterized by local operator properties. Step S2: Based on the three-stage deformation characteristics of mudstone during its fatigue life cycle, a viscoelastic-plastic composite constitutive model is constructed, consisting of Hooke elements, fractal-order elements, fractal-order Kelvin elements, and fractal-order Bingham elements with introduced damage factors connected in series. Step S3: Based on the principle of linear superposition and the assumption of small deformation, the triaxial cyclic load is decomposed into a constant static load component and a simple harmonic dynamic load component. The mechanical equilibrium conditions of the series elements include that the total stress is equal to the stress of each element and the total strain is equal to the sum of the strains of each element. Step S4: For the constant static load component, the fractal order differential equation is transformed into the standard domain analytical expression through fractal time scale transformation, and the three-dimensional strain tensor expression of each element is derived by combining the generalized Hooke's law and the framework of continuum mechanics. Step S5: For the dynamic response induced by harmonic dynamic load, the continuous time domain is discretized using the forward difference scheme, and numerical iterative formulas for strain increment of fractal-order elements and fractal-order Kelvin elements under periodic dynamic load are established. Step S6: Introduce the Drucker-Prager yield criterion as a viscoplastic flow criterion. By introducing an unsteady viscosity coefficient that decays with time, establish an iterative formula for the strain increment of the fractal Bingham element in the active state. Step S7: By conducting triaxial monotonic compression tests under multiple confining pressures and triaxial fatigue tests under different stress limits and confining pressures on mudstone samples obtained in situ on site, the rock strength characteristics and fatigue deformation curves throughout the process are obtained. Step S8: Substitute the experimental data into the constitutive equation, use a global optimization algorithm to perform multi-parameter co-fitting, determine the physical model parameters, and obtain the final surrounding rock deformation analysis model.

[0008] Preferably, step S1 specifically includes the following steps: S1.1: Using a time-scale transformation method based on local operators, the fractal order derivative formula is defined as follows:

[0009] S1.2: Extending the viscosity coefficient to fractal space, a linear mapping relationship is established between the fractal derivatives of stress and strain:

[0010] in, The fractal order is the fractal order, and its value range is 1. , The viscosity coefficient of the fractal element; S1.3: Set initial conditions Under constant axial stress Under the influence of the creep, the creep analytical equation of this unit can be obtained by integration as follows: (1-3).

[0011] Preferably, step S2 specifically includes the following steps: S2.1: To address the three-stage deformation characteristics exhibited by mudstone in indoor fatigue tests, Hooke elements were used to characterize the instantaneous strain caused by pore compression and elastic skeleton response at the moment of loading. ; S2.2: By combining fractal-order viscous elements and fractal-order Kelvin elements in series, the nonlinear deformation behavior of rocks after entering the deformation stabilization period is characterized, corresponding to strain. and ; S2.3: A fractal Bingham element with a damage coefficient introduced in series is set to activate when the cyclic load amplitude exceeds the fatigue strength threshold, generating viscoplastic strain that reflects the accelerated failure stage. .

[0012] Preferably, step S3 specifically includes the following steps: S3.1: Decoupling of axial sinusoidal loads, separating cyclic loads that evolve over time. Decomposed into:

[0013] in, As the average stress static load criterion, For dynamic load amplitude, It is the cyclic angular frequency; S3.2: Based on the small deformation assumption, the total stress-strain tensor is decomposed into a superposition of static load components and dynamic fatigue response components:

[0014] In the formula: superscripts are included. The term represents the static load component generated by the mean stress, while the term with the superscript indicates the load component. The term represents the dynamic fatigue response induced by simple harmonic dynamic load; S3.3: Based on the superposition principle of the series model, the total strain of the system is defined as the linear superposition of the tensors of the strains contributed by the elastic, viscoelastic and viscoplastic functional elements.

[0015] Preferably, step S4 specifically includes the following steps: S4.1: For differential equations containing fractal operators, introduce equivalent time variables. This is transformed into a first-order linear ordinary differential equation in the standard domain and solved analytically. S4.2: Based on the framework of continuum mechanics, the stress and strain tensors are decomposed into a spherical tensor part that reflects volume change and a deviatoric tensor part that reflects shape change, and the volume deformation is set as a purely elastic response. S4.3: Substituting the average stress and deviatoric stress components under the triaxial experimental stress path, the analytical solution for the total axial strain under three-dimensional static load is derived as follows: (4-1).

[0016] Preferably, step S5 specifically includes the following steps: S5.1: Establish the dynamic control variable coefficient equation, substitute it into the dynamic stress tensor component expression, and construct a system containing fractal time terms. A system of nonhomogeneous differential governing equations with varying coefficients; S5.2: Discretize the time domain and set a fixed time step. The first derivative of strain is approximated using a forward difference scheme, namely:

[0017] S5.3: Establish an incremental recursive algorithm to derive the dynamic axial strain iterative recursive formula for fractal-order elements and fractal-order Kelvin elements, and solve the problem of no closed analytical solution under harmonic excitation by strain accumulation.

[0018] Preferably, step S6 specifically includes the following steps: S6.1: Introduce a viscosity coefficient that decays over time:

[0019] in, This is the damage evolution rate coefficient, used to characterize the deterioration of rock bearing capacity during the accelerated phase; S6.2: Embedded plastic flow criterion, using the Drucker-Prager yield function:

[0020] As a triggering criterion for viscoplastic flow, and to establish a correlation flow rule; S6.3: Derive the damage iteration equation, and combine the fractal time scale transformation logic and forward difference scheme to derive the strain iteration formula of the fractal Bingham element under axial cyclic total load.

[0021] Preferably, step S7 specifically includes the following steps: S7.1: Standardized preparation and screening of samples. In-situ mudstone was collected from underground chambers and standard cylindrical samples were prepared. Mineral composition was analyzed by XRD diffraction and physical consistency was checked by longitudinal wave velocity test. S7.2: In 0-16 Monotonic loading experiments were conducted with multiple confining pressure levels within the range, and cohesion was extracted based on the Mohr-Coulomb criterion fitting. With internal friction angle ; S7.3: Set the stress level coefficient The values ​​are 0.7, 0.8, and 0.9, respectively, and the confining pressures are 4, 8, and 12, respectively. The lower stress limit was fixed, and the frequency was set at 0.05. The simple harmonic cyclic loading experiment was conducted to fully record the deformation data of the specimen in the three stages before instability and failure.

[0022] Preferably, step S8 specifically includes the following steps: S8.1: Construct the objective residual function, with minimizing the sum of squared residuals between the experimentally observed strain and the model-predicted strain as the optimization objective; S8.2: The differential evolution algorithm is used to search in the multidimensional parameter space to avoid the algorithm getting trapped in local optima; S8.3: Complete the calculation of the elastic modulus viscosity coefficient fractal order and damage coefficient Accurate identification of core parameters is used to form a complete surrounding rock deformation analysis model.

[0023] To achieve the second objective mentioned above, the technical solution of the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis device provided by the present invention is as follows: The compressed air energy storage power station underground lining gas storage tank surrounding rock deformation analysis device provided by the present invention includes: The model building module is used to build a deformation analysis model of the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. The feature parameter acquisition module is used to acquire the feature parameters of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station to be analyzed. The calculation module is used to input the characteristic parameters of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed into the deformation analysis model of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station. After calculation, the deformation analysis model of the underground lining gas storage cell of the compressed air energy storage power station obtains the deformation conclusion of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed.

[0024] To achieve the third objective mentioned above, the technical solution of the computer-readable storage medium provided by the present invention is as follows: The computer-readable storage medium provided by the present invention stores a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the compressed air energy storage power station underground lining gas storage tank deformation analysis program is executed by a processor, it implements the steps of the deformation analysis method for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station provided by the present invention.

[0025] To achieve the fourth objective mentioned above, the technical solution for the electronic device provided by this invention is as follows: The electronic device provided by the present invention includes a memory and a processor. The memory stores a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the processor executes the deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station, it implements the steps of the deformation analysis method for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station provided by the present invention.

[0026] This invention provides a method, apparatus, medium, and equipment for analyzing the deformation of surrounding rock in underground gas storage linings of compressed air energy storage power plants. Addressing the fatigue damage evolution of surrounding rock under long-term high pressure and large-amplitude cyclic internal pressure, a fractal-order viscoelastic-plastic fatigue constitutive model is constructed based on fractal derivative theory. Through the principle of linear superposition, the triaxial cyclic load is decomposed into a constant static load and a harmonic dynamic load. The variable-coefficient non-homogeneous differential equation is transformed into a standard domain analytical expression using fractal time-scale transformation. For the non-closed-loop solution problem under harmonic dynamic load, a forward difference scheme is introduced to achieve numerical iteration of strain increments. Strength parameters are extracted based on indoor triaxial rock compression experiments, and parameter identification is performed in conjunction with triaxial fatigue experiments. This invention utilizes the local operator properties of fractal derivatives to avoid the convolution calculations of traditional fractional-order models, enabling accurate characterization of the instantaneous, stable, and accelerated deformation stages of rock under cyclic loading. Attached Figure Description

[0027] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Appendix Figure 1 A flowchart illustrating the overall steps of a method for analyzing the deformation of the surrounding rock of an underground lining gas storage tank in a compressed air energy storage power station, as provided in an embodiment of the present invention. Appendix Figure 2 The flowchart illustrates the overall steps of constructing a deformation analysis model for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station, as provided in this embodiment of the invention. Appendix Figure 3 A schematic diagram of the signal flow relationship between the functional modules in the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis device provided in an embodiment of the present invention; Appendix Figure 4 A schematic diagram of the structure of an emotion recognition device for the hardware operating environment provided in an embodiment of the present invention. Detailed Implementation

[0028] To address the problems existing in the prior art, this invention provides a method, device, medium, and equipment for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station. It is based on the fractal derivative theory of the deformation analysis model and implementation method of the surrounding rock of the gas storage tank, and derives its constitutive equation under triaxial cyclic loading. The aim is to accurately describe the fatigue damage evolution law of the surrounding rock under long-term high pressure and large amplitude internal pressure conditions, thus making it more suitable for practical use.

[0029] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation methods, structures, features, and effects of the method, apparatus, medium, and equipment for analyzing the surrounding rock deformation of the underground lining gas storage tank of a compressed air energy storage power station according to the present invention. In the following description, different "embodiments" or "embodiments" do not necessarily refer to the same embodiment. Furthermore, features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0030] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships, such as A and / or B. Specifically, it can mean that A and B can be included at the same time, A can exist alone, or B can exist alone, and any of the above three situations can be met.

[0031] Deformation Analysis Method of Surrounding Rock of Underground Liner Gas Storage Cell in Compressed Air Energy Storage Power Station See appendix Figure 1 and attached Figure 2 The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station provided in this embodiment of the invention includes the following steps: The specific steps for constructing a deformation analysis model of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station are as follows: S1: For the viscoelastic response of rocks under cyclic loading, a fractal viscous element is defined based on the fractal derivative theory, a linear mapping relationship between stress and strain fractal derivatives is established, and the nonlinear characteristics of rock rheology are characterized by local operator properties.

[0032] S1.1: The fractal derivative is a time-scale transformation method based on local operators, which differs from the traditional fractional derivative theory. Its advantage lies in that it does not involve convolution integrals, significantly improving computational efficiency while maintaining accuracy. The mathematical definition of the fractal derivative is as follows:

[0033] In the formula: This is standard Euclidean time; is the order of the fractal derivative.

[0034] S1.2: Based on the above definition, a fractal-order element reflecting the nonlinear rheological behavior of rocks can be constructed. This element establishes a linear mapping relationship between the fractal-order derivatives of stress and strain by extending the traditional integer-order viscosity coefficient to fractal space.

[0035] in, The range of values ​​satisfies In terms of physical mechanisms, this is achieved by introducing an equivalent time variable. It can transform complex fractal differential equations into standard form integer-order linear differential equations for processing; S1.3: Under constant axial stress Under the influence of the equation (1-2), by integrating the equation and considering the initial conditions, The creep analytical equation for this fractal element can be obtained as follows:

[0036] S2: In order to establish such Figure 2 The constitutive model shown can describe the mechanical behavior of rock fatigue deformation throughout the entire process. Based on the study of the fatigue deformation curve of mudstone under cyclic loading, the sample exhibits significant stage characteristics throughout its entire life cycle.

[0037] S2.1: At the instant of axial load application, the compression of pores within the rock and the response of the elastic skeleton lead to significant instantaneous strain. This process is reversible and requires quantitative description using Hooke elements in mechanical terms. S2.2: As the number of cycles increases, the rock enters a period of stable deformation. At lower cyclic stress levels, the evolution of microcracks tends to be gradual, and the strain rate usually tends to a non-zero constant. Since traditional linear elements are difficult to accurately characterize the nonlinear rheological properties of rocks, fractal elements and fractal Kelvin elements need to be introduced to characterize their nonlinear stable deformation behavior over time. S2.3: Once the cyclic stress amplitude exceeds the fatigue limit of the rock, internal damage will gradually accumulate and eventually lead to rock failure, macroscopically manifested as a drastic jump in strain rate and structural instability. This stage requires the introduction of fractal-order Bingham elements with damage coefficients to reflect its nonlinear accelerated deformation characteristics.

[0038] S3: Axial cyclic load applied to the specimen during indoor triaxial fatigue testing of rock. It exhibits sinusoidal fluctuation characteristics over time:

[0039] In the formula: and These represent the upper and lower limits of cyclic stress, respectively. ω is the cyclic angular frequency of the load.

[0040] S3.1: Based on the principle of linear superposition, the cyclic load that evolves with time in equation (3-1) can be decomposed into a constant static load component. With simple harmonic dynamic load components Composite forms:

[0041] in, As the average stress static load criterion, For dynamic load amplitude; S3.2: Based on the small deformation assumption, complex axial stress and strain tensors and Both can be decomposed into a superposition of static load and simple harmonic dynamic load:

[0042] In the formula: superscripts are included. The term represents the static load component generated by the mean stress, while the term with the superscript indicates the load component. The term represents the dynamic fatigue response induced by simple harmonic dynamic load; S3.3: According to the superposition principle of the series mechanics model, the total stress of the system is equal to that of each component, while the total strain is equal to that of each component. The linear superposition of strains contributing to each functional element:

[0043] In the formula: For instantaneous elastic strain; and The viscoelastic strain of the fractal-order element and the fractal-order Kelvin element; To characterize the viscoplastic strain of the fractal-order Bingham element as it enters the accelerated failure stage.

[0044] S4: Under constant axial stress Under the influence of [the specific function], the derivation process of the one-dimensional analytical expression of the combinatorial model is as follows: S4.1: The strain generated by a Hooke element depends only on the current stress level, exhibiting a time-independent instantaneous characteristic. Its constitutive relation is expressed as:

[0045] In the formula, Let be the elastic modulus of the Hooke element.

[0046] According to equation (1-3), the power-law response equation of the fractal element under constant stress is:

[0047] Here, and These represent the viscosity coefficient and fractal order of the fractal element, respectively, and control the nonlinear growth characteristics of the creep curve.

[0048] The one-dimensional mechanical equilibrium equation of a fractal-order Kelvin element is defined as follows:

[0049] In the formula, and The viscosity coefficient and fractal order represent the fractal element. Let be the elastic modulus of the Hooke element connected in parallel. To solve this differential equation involving fractal-order operators, a fractal time variable is introduced. By performing a scaling transformation, it is converted into a standard first-order linear ordinary differential equation:

[0050] Combined with initial strain-free conditions The creep equation that evolves over time can be obtained by using the integral factor method:

[0051] S4.2: Under three-dimensional conditions, based on the framework of continuum mechanics, the stress and strain tensors are decomposed into a spherical tensor component reflecting volume changes and a partial tensor component reflecting shape changes.

[0052] According to the generalized Hooke's law, the strain tensor of the Hooke element is in the form of:

[0053] in, and These are the shear modulus and bulk modulus of the Hooke element, respectively, and their relationship with the material's elastic modulus. and Poisson's ratio The conversion relationship follows the basic definition of elasticity:

[0054] In rheological assumptions, the volumetric deformation of rocks is generally considered to be purely elastic and driven by spherical stress. However, the complex rheological properties are mainly manifested in the shear deformation excited by the deviatoric stress tensor. Introducing a three-dimensional equivalent viscosity coefficient, the constitutive relation of the fractal element is:

[0055] In the formula, The equivalent viscosity coefficient under three-dimensional conditions, which is related to Poisson's ratio. With one-dimensional viscosity coefficient It has the following conversion relationship:

[0056] By analogy with one-dimensional integral solving, the constitutive relation of the fractal-order Kelvin element is:

[0057] S4.3: Mean stress caused by static load under the stress path in a triaxial fatigue test. With axial deviatoric stress tensor components The calculations are as follows:

[0058] By combining the strain contributions of each functional component, the total axial strain under three-dimensional static load is finally derived. Analytical solution evolving over time:

[0059] S5: Regarding the strain response of each component under simple harmonic dynamic load, the specific steps are as follows: S5.1: Mean stress tensor caused by simple harmonic dynamic load With axial deviatoric stress tensor They can be represented as:

[0060] Substituting into the generalized Hooke's law, we obtain the dynamic axial strain of the Hooke element as:

[0061] S5.2: Substituting equations (5-1) and (5-2) into the constitutive equation of the fractal element and simplifying, we get:

[0062] Because the equation coefficients contain fractal time terms The above equation is essentially a typical nonhomogeneous differential equation with varying coefficients, making it difficult to obtain an analytical solution using elementary functions in closed form. A fixed time step is set as... Then the first The time point corresponding to each time step is The first derivative of strain is approximated using a forward difference scheme:

[0063] S5.3: Substituting equation (5-5) into the constitutive equation of the fractal element, we obtain its strain iteration formula as follows:

[0064] Similarly, the strain iteration formula for the fractal Kelvin element is:

[0065] S6: When the amplitude of the axial cyclic stress exceeds the fatigue strength of the rock, the fractal Bingham element is activated, defining the super-yield stress under one-dimensional stress. for:

[0066] S6.1: To characterize the nonlinear degradation of rock bearing capacity during the accelerated deformation stage, a viscosity coefficient that decays over time is introduced:

[0067] in, The initial viscosity coefficient, As a damage variable, it is used to characterize the deterioration of rock bearing capacity during the accelerated phase. This represents the fractal order.

[0068] S6.2: Under complex stress states, the yielding behavior of rock is influenced by both spherical stress and deviatoric stress. The Drucker-Prager yield function is used as the criterion for judging viscoplastic flow.

[0069] in, The second invariant of the stress deviatoric tensor, The first invariant of stress; parameter and The internal friction angles with the rock respectively and cohesion Related.

[0070] Introducing the Heaviside function and the positive part function:

[0071] According to the correlation flow rule, when Viscoplastic flow occurs. Combining the fractal derivative, the constitutive equation for a fractal Bingham element under three-dimensional conditions is expressed as:

[0072] S6.3: Under the stress path of a conventional triaxial test, the axial flow direction vector is:

[0073] This allows us to construct the three-dimensional constitutive differential equation of the element:

[0074] Combining equation (5-5), the strain iteration formula for the fractal Bingham element is as follows:

[0075] S7: By conducting triaxial monotonic compression tests under multiple confining pressures and triaxial fatigue tests under different stress limits and confining pressures on mudstone samples obtained in situ, the rock strength characteristics and fatigue deformation curves throughout the process are obtained. Specifically, the following steps are included: S7.1: Standardized preparation and screening of samples. In-situ mudstone was collected from underground chambers and standard cylindrical samples were prepared. Mineral composition was analyzed by XRD diffraction and physical consistency was checked by longitudinal wave velocity test. S7.2: In 0-16 Monotonic loading experiments were conducted with multiple confining pressure levels within the range, and cohesion was extracted based on the Mohr-Coulomb criterion fitting. With internal friction angle ; S7.3: Set the stress level coefficient The values ​​are 0.7, 0.8, and 0.9, respectively, and the confining pressures are 4, 8, and 12, respectively. The lower stress limit was fixed, and the frequency was set at 0.05. The simple harmonic cyclic loading experiment was conducted to fully record the deformation data of the specimen in the three stages before instability and failure.

[0076] S8: Substitute the experimental data into the constitutive equations, use a global optimization algorithm to perform multi-parameter co-fitting, determine the physical model parameters, and obtain the final surrounding rock deformation analysis model.

[0077] S8.1: Construct the objective residual function, with minimizing the sum of squared residuals between the experimentally observed strain and the model-predicted strain as the optimization objective; S8.2: The differential evolution algorithm is used to search in the multidimensional parameter space to avoid the algorithm getting trapped in local optima; S8.3: Complete the calculation of the elastic modulus viscosity coefficient fractal order and damage coefficient The accurate identification of core parameters ultimately leads to the formation of a complete surrounding rock deformation analysis model.

[0078] This invention provides a method for analyzing the deformation of surrounding rock in underground gas storage linings of compressed air energy storage power plants. Addressing the fatigue damage evolution of surrounding rock under long-term high pressure and large-amplitude cyclic internal pressure, a fractal-order viscoelastic-plastic fatigue constitutive model is constructed based on fractal derivative theory. Through the principle of linear superposition, the triaxial cyclic load is decomposed into a constant static load and a harmonic dynamic load. The variable-coefficient non-homogeneous differential equation is transformed into a standard domain analytical expression using fractal time-scale transformation. For the non-closed-loop solution problem under harmonic dynamic load, a forward difference scheme is introduced to achieve numerical iteration of strain increments. Strength parameters are extracted based on indoor triaxial rock compression experiments, and parameter identification is performed in conjunction with triaxial fatigue experiments. This invention utilizes the local operator properties of fractal derivatives to avoid the convolution calculations of traditional fractional-order models, enabling accurate characterization of the instantaneous, stable, and accelerated deformation stages of rock under cyclic loading.

[0079] Deformation Analysis Device for Surrounding Rock of Underground Liner Gas Storage Cell in Compressed Air Energy Storage Power Station See appendix Figure 3 The compressed air energy storage power station underground lining gas storage tank surrounding rock deformation analysis device provided by the present invention includes: The model building module is used to construct a deformation analysis model of the surrounding rock of the underground gas storage lining of a compressed air energy storage power station. The specific method for constructing this model includes the following steps: S1: For the viscoelastic response of rocks under cyclic loading, a fractal viscous element is defined based on the fractal derivative theory, a linear mapping relationship between stress and strain fractal derivatives is established, and the nonlinear characteristics of rock rheology are characterized by local operator properties.

[0080] S1.1: The fractal derivative is a time-scale transformation method based on local operators, which differs from the traditional fractional derivative theory. Its advantage lies in that it does not involve convolution integrals, significantly improving computational efficiency while maintaining accuracy. The mathematical definition of the fractal derivative is as follows:

[0081] In the formula: This is standard Euclidean time; is the order of the fractal derivative.

[0082] S1.2: Based on the above definition, a fractal-order element reflecting the nonlinear rheological behavior of rocks can be constructed. This element establishes a linear mapping relationship between the fractal-order derivatives of stress and strain by extending the traditional integer-order viscosity coefficient to fractal space.

[0083] in, The range of values ​​satisfies In terms of physical mechanisms, this is achieved by introducing an equivalent time variable. It can transform complex fractal differential equations into standard form integer-order linear differential equations for processing; S1.3: Under constant axial stress Under the influence of the equation (1-2), by integrating the equation and considering the initial conditions, The creep analytical equation for this fractal element can be obtained as follows:

[0084] S2: In order to establish such Figure 2 The constitutive model shown can describe the mechanical behavior of rock fatigue deformation throughout the entire process. Based on the study of the fatigue deformation curve of mudstone under cyclic loading, the sample exhibits significant stage characteristics throughout its entire life cycle.

[0085] S2.1: At the instant of axial load application, the compression of pores within the rock and the response of the elastic skeleton lead to significant instantaneous strain. This process is reversible and requires quantitative description using Hooke elements in mechanical terms. S2.2: As the number of cycles increases, the rock enters a period of stable deformation. At lower cyclic stress levels, the evolution of microcracks tends to be gradual, and the strain rate usually tends to a non-zero constant. Since traditional linear elements are difficult to accurately characterize the nonlinear rheological properties of rocks, fractal elements and fractal Kelvin elements need to be introduced to characterize their nonlinear stable deformation behavior over time. S2.3: Once the cyclic stress amplitude exceeds the fatigue limit of the rock, internal damage will gradually accumulate and eventually lead to rock failure, macroscopically manifested as a drastic jump in strain rate and structural instability. This stage requires the introduction of fractal-order Bingham elements with damage coefficients to reflect its nonlinear accelerated deformation characteristics.

[0086] S3: Axial cyclic load applied to the specimen during indoor triaxial fatigue testing of rock. It exhibits sinusoidal fluctuation characteristics over time:

[0087] In the formula: and These represent the upper and lower limits of cyclic stress, respectively. ω is the cyclic angular frequency of the load.

[0088] S3.1: Based on the principle of linear superposition, the cyclic load that evolves with time in equation (3-1) can be decomposed into a constant static load component. With simple harmonic dynamic load components Composite forms:

[0089] in, As the average stress static load criterion, For dynamic load amplitude; S3.2: Based on the small deformation assumption, complex axial stress and strain tensors and Both can be decomposed into a superposition of static load and simple harmonic dynamic load:

[0090] In the formula: superscripts are included. The term represents the static load component generated by the mean stress, while the term with the superscript indicates the load component. The term represents the dynamic fatigue response induced by simple harmonic dynamic load; S3.3: According to the superposition principle of the series mechanics model, the total stress of the system is equal to that of each component, while the total strain is equal to that of each component. The linear superposition of strains contributing to each functional element:

[0091] In the formula: For instantaneous elastic strain; and The viscoelastic strain of the fractal-order element and the fractal-order Kelvin element; To characterize the viscoplastic strain of the fractal-order Bingham element as it enters the accelerated failure stage.

[0092] S4: Under constant axial stress Under the influence of [the specific function], the derivation process of the one-dimensional analytical expression of the combinatorial model is as follows: S4.1: The strain generated by a Hooke element depends only on the current stress level, exhibiting a time-independent instantaneous characteristic. Its constitutive relation is expressed as:

[0093] In the formula, Let be the elastic modulus of the Hooke element.

[0094] According to equation (1-3), the power-law response equation of the fractal element under constant stress is:

[0095] Here, and These represent the viscosity coefficient and fractal order of the fractal element, respectively, and control the nonlinear growth characteristics of the creep curve.

[0096] The one-dimensional mechanical equilibrium equation of a fractal-order Kelvin element is defined as follows:

[0097] In the formula, and The viscosity coefficient and fractal order represent the fractal element. Let be the elastic modulus of the Hooke element connected in parallel. To solve this differential equation involving fractal-order operators, a fractal time variable is introduced. By performing a scaling transformation, it is converted into a standard first-order linear ordinary differential equation:

[0098] Combined with initial strain-free conditions The creep equation that evolves over time can be obtained by using the integral factor method:

[0099] S4.2: Under three-dimensional conditions, based on the framework of continuum mechanics, the stress and strain tensors are decomposed into a spherical tensor component reflecting volume changes and a partial tensor component reflecting shape changes.

[0100] According to the generalized Hooke's law, the strain tensor of the Hooke element is in the form of:

[0101] in, and These are the shear modulus and bulk modulus of the Hooke element, respectively, and their relationship with the material's elastic modulus. and Poisson's ratio The conversion relationship follows the basic definition of elasticity:

[0102] In rheological assumptions, the volumetric deformation of rocks is generally considered to be purely elastic and driven by spherical stress. However, the complex rheological properties are mainly manifested in the shear deformation excited by the deviatoric stress tensor. Introducing a three-dimensional equivalent viscosity coefficient, the constitutive relation of the fractal element is:

[0103] In the formula, The equivalent viscosity coefficient under three-dimensional conditions, which is related to Poisson's ratio. With one-dimensional viscosity coefficient It has the following conversion relationship:

[0104] By analogy with one-dimensional integral solving, the constitutive relation of the fractal-order Kelvin element is:

[0105] S4.3: Mean stress caused by static load under the stress path in a triaxial fatigue test. With axial deviatoric stress tensor components The calculations are as follows:

[0106] By combining the strain contributions of each functional component, the total axial strain under three-dimensional static load is finally derived. Analytical solution evolving over time:

[0107] S5: Regarding the strain response of each component under simple harmonic dynamic load, the specific steps are as follows: S5.1: Mean stress tensor caused by simple harmonic dynamic load With axial deviatoric stress tensor They can be represented as:

[0108] Substituting into the generalized Hooke's law, we obtain the dynamic axial strain of the Hooke element as:

[0109] S5.2: Substituting equations (5-1) and (5-2) into the constitutive equation of the fractal element and simplifying, we get:

[0110] Because the equation coefficients contain fractal time terms The above equation is essentially a typical nonhomogeneous differential equation with varying coefficients, making it difficult to obtain an analytical solution using elementary functions in closed form. A fixed time step is set as... Then the first The time point corresponding to each time step is The first derivative of strain is approximated using a forward difference scheme:

[0111] S5.3: Substituting equation (5-5) into the constitutive equation of the fractal element, we obtain its strain iteration formula as follows:

[0112] Similarly, the strain iteration formula for the fractal Kelvin element is:

[0113] S6: When the amplitude of the axial cyclic stress exceeds the fatigue strength of the rock, the fractal Bingham element is activated, defining the super-yield stress under one-dimensional stress. for:

[0114] S6.1: To characterize the nonlinear degradation of rock bearing capacity during the accelerated deformation stage, a viscosity coefficient that decays over time is introduced:

[0115] in, The initial viscosity coefficient, As a damage variable, it is used to characterize the deterioration of rock bearing capacity during the accelerated phase. This represents the fractal order.

[0116] S6.2: Under complex stress states, the yielding behavior of rock is influenced by both spherical stress and deviatoric stress. The Drucker-Prager yield function is used as the criterion for judging viscoplastic flow.

[0117] in, The second invariant of the stress deviatoric tensor, The first invariant of stress; parameter and The internal friction angles with the rock respectively and cohesion Related.

[0118] Introducing the Heaviside function and the positive part function:

[0119] According to the correlation flow rule, when Viscoplastic flow occurs. Combining the fractal derivative, the constitutive equation for a fractal Bingham element under three-dimensional conditions is expressed as:

[0120] S6.3: Under the stress path of a conventional triaxial test, the axial flow direction vector is:

[0121] This allows us to construct the three-dimensional constitutive differential equation of the element:

[0122] Combining equation (5-5), the strain iteration formula for the fractal Bingham element is as follows:

[0123] S7: By conducting triaxial monotonic compression tests under multiple confining pressures and triaxial fatigue tests under different stress limits and confining pressures on mudstone samples obtained in situ, the rock strength characteristics and fatigue deformation curves throughout the process are obtained. Specifically, the following steps are included: S7.1: Standardized preparation and screening of samples. In-situ mudstone was collected from underground chambers and standard cylindrical samples were prepared. Mineral composition was analyzed by XRD diffraction and physical consistency was checked by longitudinal wave velocity test. S7.2: In 0-16 Monotonic loading experiments were conducted with multiple confining pressure levels within the range, and cohesion was extracted based on the Mohr-Coulomb criterion fitting. With internal friction angle ; S7.3: Set the stress level coefficient The values ​​are 0.7, 0.8, and 0.9, respectively, and the confining pressures are 4, 8, and 12, respectively. The lower stress limit was fixed, and the frequency was set at 0.05. The simple harmonic cyclic loading experiment was conducted to fully record the deformation data of the specimen in the three stages before instability and failure.

[0124] S8: Substitute the experimental data into the constitutive equations, use a global optimization algorithm to perform multi-parameter co-fitting, determine the physical model parameters, and obtain the final surrounding rock deformation analysis model.

[0125] S8.1: Construct the objective residual function, with minimizing the sum of squared residuals between the experimentally observed strain and the model-predicted strain as the optimization objective; S8.2: The differential evolution algorithm is used to search in the multidimensional parameter space to avoid the algorithm getting trapped in local optima; S8.3: Complete the calculation of the elastic modulus viscosity coefficient fractal order and damage coefficient The accurate identification of core parameters ultimately leads to the formation of a complete surrounding rock deformation analysis model.

[0126] The feature parameter acquisition module is used to acquire the feature parameters of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station to be analyzed. The calculation module is used to input the characteristic parameters of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed into the deformation analysis model of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station. After calculation, the deformation analysis model of the underground lining gas storage cell of the compressed air energy storage power station obtains the deformation conclusion of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed.

[0127] This invention provides a deformation analysis device for the surrounding rock of underground gas storage lining in compressed air energy storage power stations. Addressing the fatigue damage evolution of the surrounding rock under long-term high pressure and large-amplitude cyclic internal pressure, a fractal-order viscoelastic-plastic fatigue constitutive model is constructed based on fractal derivative theory. Through the principle of linear superposition, the triaxial cyclic load is decomposed into a constant static load and a harmonic dynamic load. The variable-coefficient non-homogeneous differential equation is transformed into a standard domain analytical expression using fractal time-scale transformation. For the non-closed-loop solution problem under harmonic dynamic load, a forward difference scheme is introduced to achieve numerical iteration of strain increments. Strength parameters are extracted based on indoor triaxial rock compression experiments, and parameter identification is performed in conjunction with triaxial fatigue experiments. This invention utilizes the local operator properties of fractal derivatives to avoid the convolution calculations of traditional fractional-order models, enabling accurate characterization of the instantaneous, stable, and accelerated deformation stages of rock under cyclic loading.

[0128] Computer-readable storage media The computer-readable storage medium provided by the present invention stores a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the compressed air energy storage power station underground lining gas storage tank deformation analysis program is executed by a processor, it implements the steps of the deformation analysis method for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station provided by the present invention.

[0129] The computer-readable storage medium provided by this invention provides a program for analyzing the deformation of the surrounding rock of the underground gas storage lining of a compressed air energy storage power station. When executed by a processor, this program addresses the fatigue damage evolution of the surrounding rock under long-term high pressure and large amplitude cyclic internal pressure. Based on fractal derivative theory, a fractal-order viscoelastic-plastic fatigue constitutive model is constructed. Through the principle of linear superposition, the triaxial cyclic load is decomposed into a constant static load and a harmonic dynamic load. The variable-coefficient non-homogeneous differential equation is transformed into a standard domain analytical expression using fractal time-scale transformation. For the non-closed-loop solution problem under harmonic dynamic load, a forward difference scheme is introduced to achieve numerical iteration of strain increments. Strength parameters are extracted based on indoor triaxial rock compression experiments, and parameter identification is performed in conjunction with triaxial fatigue experiments. This invention utilizes the local operator properties of fractal derivatives to avoid the convolution calculations of traditional fractional-order models, enabling accurate characterization of the instantaneous, stable, and accelerated deformation stages of rock under cyclic loading.

[0130] electronic devices The electronic device provided by the present invention includes a memory and a processor. The memory stores a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the processor executes the deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station, it implements the steps of the deformation analysis method for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station provided by the present invention.

[0131] The deformation analysis program for the surrounding rock of the underground gas storage lining of a compressed air energy storage power station, stored in the memory of the electronic device provided by this invention, is executed by a processor. Based on fractal derivative theory, a fractal-order viscoelastic-plastic fatigue constitutive model is constructed to address the fatigue damage evolution of the surrounding rock under long-term high pressure and large amplitude cyclic internal pressure. Through the principle of linear superposition, the triaxial cyclic load is decomposed into a constant static load and a harmonic dynamic load. The variable-coefficient non-homogeneous differential equation is transformed into a standard domain analytical expression using fractal time-scale transformation. For the non-closed-loop solution problem under harmonic dynamic load, a forward difference scheme is introduced to achieve numerical iteration of strain increments. Strength parameters are extracted based on indoor triaxial rock compression experiments, and parameter identification is performed in conjunction with triaxial fatigue experiments. This invention utilizes the local operator properties of fractal derivatives to avoid the convolution calculations of traditional fractional-order models, enabling accurate characterization of the instantaneous, stable, and accelerated deformation stages of rock under cyclic loading.

[0132] See appendix Figure 4 , attached Figure 4 This is a schematic diagram of the structure of the surrounding rock deformation analysis equipment for the underground lining gas storage tank of a compressed air energy storage power station, which is part of the hardware operating environment of the embodiment of the present invention.

[0133] As attached Figure 4As shown, the deformation analysis equipment for the surrounding rock of the underground gas storage lining of the compressed air energy storage power station may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen and an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed random access memory (RAM) or a stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0134] Those skilled in the art will understand that the appendix Figure 4 The structure shown does not constitute a limitation on the surrounding rock deformation analysis equipment for the underground lining gas storage tank of a compressed air energy storage power station. It may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0135] As attached Figure 4 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station.

[0136] In the appendix Figure 4 In the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis equipment shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and memory 1005 in the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis equipment of the present invention can be set in the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis equipment. The compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis equipment calls the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis program stored in memory 1005 through processor 1001, and executes the compressed air energy storage power station underground lining gas storage surrounding rock deformation analysis method provided in the embodiment of the present invention.

[0137] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0138] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station, characterized in that, Includes the following steps: Construct a deformation analysis model for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station; Obtain characteristic parameters of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station to be analyzed; The characteristic parameters of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed are input into the deformation analysis model of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station. After calculation, the deformation conclusion of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed is obtained.

2. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 1, characterized in that, The specific steps for constructing the deformation analysis model of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station include: Step S1: For the viscoelastic response of rock under cyclic loading, a fractal viscous element is defined based on the fractal derivative theory, and a linear mapping relationship between stress and strain fractal derivatives is established. The nonlinear characteristics of rock rheology are characterized by local operator properties. Step S2: Based on the three-stage deformation characteristics of mudstone during its fatigue life cycle, a viscoelastic-plastic composite constitutive model is constructed, consisting of Hooke elements, fractal-order elements, fractal-order Kelvin elements, and fractal-order Bingham elements with introduced damage factors connected in series. Step S3: Based on the principle of linear superposition and the assumption of small deformation, the triaxial cyclic load is decomposed into a constant static load component and a simple harmonic dynamic load component. The mechanical equilibrium conditions of the series elements include that the total stress is equal to the stress of each element and the total strain is equal to the sum of the strains of each element. Step S4: For the constant static load component, the fractal order differential equation is transformed into the standard domain analytical expression through fractal time scale transformation, and the three-dimensional strain tensor expression of each element is derived by combining the generalized Hooke's law and the framework of continuum mechanics. Step S5: For the dynamic response induced by harmonic dynamic load, the continuous time domain is discretized using the forward difference scheme, and numerical iterative formulas for strain increment of fractal-order elements and fractal-order Kelvin elements under periodic dynamic load are established. Step S6: Introduce the Drucker-Prager yield criterion as a viscoplastic flow criterion. By introducing an unsteady viscosity coefficient that decays with time, establish an iterative formula for the strain increment of the fractal Bingham element in the active state. Step S7: By conducting triaxial monotonic compression tests under multiple confining pressures and triaxial fatigue tests under different stress limits and confining pressures on mudstone samples obtained in situ on site, the rock strength characteristics and fatigue deformation curves throughout the process are obtained. Step S8: Substitute the experimental data into the constitutive equation, use a global optimization algorithm to perform multi-parameter co-fitting, determine the physical model parameters, and obtain the final surrounding rock deformation analysis model.

3. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 2, characterized in that, Step S1 specifically includes the following steps: S1.1: Using a time-scale transformation method based on local operators, the fractal order derivative formula is defined as follows: S1.2: Extending the viscosity coefficient to fractal space, a linear mapping relationship is established between the fractal derivatives of stress and strain: in, The fractal order is the fractal order, and its value range is 1. , The viscosity coefficient of the fractal element; S1.3: Set initial conditions Under constant axial stress Under the influence of the creep, the creep analytical equation of this unit can be obtained by integration as follows: (1-3)。 4. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 2, characterized in that, Step S2 specifically includes the following steps: S2.1: To address the three-stage deformation characteristics exhibited by mudstone in indoor fatigue tests, Hooke elements were used to characterize the instantaneous strain caused by pore compression and elastic skeleton response at the moment of loading. ; S2.2: By combining fractal-order viscous elements and fractal-order Kelvin elements in series, the nonlinear deformation behavior of rocks after entering the deformation stabilization period is characterized, corresponding to strain. and ; S2.3: A fractal Bingham element with a damage coefficient introduced in series is set to activate when the cyclic load amplitude exceeds the fatigue strength threshold, generating viscoplastic strain that reflects the accelerated failure stage. .

5. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 1, characterized in that, Step S3 specifically includes the following steps: S3.1: Decoupling of axial sinusoidal loads, separating cyclic loads that evolve over time. Decomposed into: in, As the average stress static load criterion, For dynamic load amplitude, It is the cyclic angular frequency; S3.2: Based on the small deformation assumption, the total stress-strain tensor is decomposed into a superposition of static load components and dynamic fatigue response components: In the formula: superscripts are included. The term represents the static load component generated by the mean stress, while the term with the superscript indicates the load component. The term represents the dynamic fatigue response induced by simple harmonic dynamic load; S3.3: Based on the superposition principle of the series model, the total strain of the system is defined as the linear superposition of the tensors of the strains contributed by the elastic, viscoelastic and viscoplastic functional elements.

6. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 1, characterized in that, Step S4 specifically includes the following steps: S4.1: For differential equations containing fractal operators, introduce equivalent time variables. This is transformed into a first-order linear ordinary differential equation in the standard domain and solved analytically. S4.2: Based on the framework of continuum mechanics, the stress and strain tensors are decomposed into a spherical tensor part that reflects volume change and a deviatoric tensor part that reflects shape change, and the volume deformation is set as a purely elastic response. S4.3: Substituting the average stress and deviatoric stress components under the triaxial experimental stress path, the analytical solution for the total axial strain under three-dimensional static load is derived as follows: (4-1)。 7. The method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank in a compressed air energy storage power station according to claim 1, characterized in that, Step S5 specifically includes the following steps: S5.1: Establish the dynamic control variable coefficient equation, substitute it into the dynamic stress tensor component expression, and construct a system containing fractal time terms. A system of nonhomogeneous differential governing equations with varying coefficients; S5.2: Discretize the time domain and set a fixed time step. The first derivative of strain is approximated using a forward difference scheme, namely: S5.3: Establish an incremental recursive algorithm to derive the dynamic axial strain iterative recursive formula for fractal-order elements and fractal-order Kelvin elements, and solve the problem of no closed analytical solution under harmonic excitation by strain accumulation; Preferably, step S6 specifically includes the following steps: S6.1: Introduce a viscosity coefficient that decays over time: in, This is the damage evolution rate coefficient, used to characterize the deterioration of rock bearing capacity during the accelerated phase; S6.2: Embedded plastic flow criterion, using the Drucker-Prager yield function: As a triggering criterion for viscoplastic flow, and to establish a correlation flow rule; S6.3: Derive the damage iteration equation, and combine the fractal time scale transformation logic and forward difference scheme to derive the strain iteration formula of the fractal Bingham element under the action of axial cyclic total load. Preferably, step S7 specifically includes the following steps: S7.1: Standardized preparation and screening of samples. In-situ mudstone was collected from underground chambers and standard cylindrical samples were prepared. Mineral composition was analyzed by XRD diffraction and physical consistency was checked by longitudinal wave velocity test. S7.2: In 0-16 Monotonic loading experiments were conducted with multiple confining pressure levels within the range, and cohesion was extracted based on the Mohr-Coulomb criterion fitting. With internal friction angle ; S7.3: Set the stress level coefficient The values ​​are 0.7, 0.8, and 0.9, respectively, and the confining pressures are 4, 8, and 12, respectively. The lower stress limit was fixed, and the frequency was set at 0.

05. The simple harmonic cyclic loading experiment was used to fully record the three-stage deformation data of the specimen before instability and failure. Preferably, step S8 specifically includes the following steps: S8.1: Construct the objective residual function, with minimizing the sum of squared residuals between the experimentally observed strain and the model-predicted strain as the optimization objective; S8.2: The differential evolution algorithm is used to search in the multidimensional parameter space to avoid the algorithm getting trapped in local optima; S8.3: Complete the calculation of the elastic modulus viscosity coefficient fractal order and damage coefficient Accurate identification of core parameters is used to form a complete surrounding rock deformation analysis model.

8. A device for analyzing the deformation of the surrounding rock of an underground gas storage lining in a compressed air energy storage power station, characterized in that, include: The model building module is used to build a deformation analysis model of the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. The feature parameter acquisition module is used to acquire the feature parameters of the surrounding rock of the underground lining gas storage tank of the compressed air energy storage power station to be analyzed. The calculation module is used to input the characteristic parameters of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed into the deformation analysis model of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station. After calculation, the deformation analysis model of the underground lining gas storage cell of the compressed air energy storage power station obtains the deformation conclusion of the surrounding rock of the underground lining gas storage cell of the compressed air energy storage power station to be analyzed.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a deformation analysis program for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the compressed air energy storage power station underground lining gas storage tank deformation analysis program is executed by the processor, it implements the steps of the deformation analysis method for the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station as described in any one of claims 1-7.

10. An electronic device, characterized in that, The device includes a memory and a processor. The memory stores a program for analyzing the deformation of the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station. When the processor executes the program, it implements the steps of the method for analyzing the deformation of the surrounding rock of the underground lining gas storage tank of a compressed air energy storage power station as described in any one of claims 1-7.

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