Method for determining the operating pressure of a compressed air energy storage cavern

Abstract

The application discloses a kind of compressed air energy storage cavern operating pressure determination method, comprising the following steps: establishing the elastic mechanics plane strain model of surrounding rock-lining-sealing layer composite structure, deducing the analytical solution of elastic stress and displacement of composite structure;Determine the upper limit of cyclic internal pressure;Introduce the spatial heterogeneity function of surrounding rock parameter, deduce the elastoplastic stress and plastic zone radius expression of composite structure;Introduce the fatigue damage evolution equation to correct rock mass strength parameter, based on the plastic zone radius control condition, solve lower limit pressure.The method can simultaneously utilize initial geostress to constrain surrounding rock deformation and quantify the attenuation of rock mass parameters caused by long-term cyclic loading, while ensuring that surrounding rock does not produce tensile failure and the expansion of plastic zone is controllable, the best operating pressure range and amplitude of compressed air energy storage cavern in the whole life cycle of up to 30 years are accurately quantified, so as to ensure the long-term sealing and safety of the structure, effectively optimize the design parameters, and improve the engineering economy.

Description

Technical Field

[0001] This invention relates to the fields of underground space engineering and large-scale physical energy storage technology, specifically to a method for determining the operating pressure of an underground compressed gas energy storage cavern that takes into account initial geostress constraints, spatial heterogeneity of rock mass, and fatigue damage throughout the entire life cycle. Background Technology

[0002] Compressed air energy storage (CASS) is a large-scale physical energy storage method that compresses and stores air in underground spaces during periods of low grid load, and releases the high-pressure air to drive turbines for power generation during periods of high load. This technology is of great significance for improving grid stability and promoting the consumption of renewable energy. Among these technologies, underground rock-lined caverns have become an important development direction for CASS power plant storage space due to their large storage capacity, flexible site selection, low construction cost, and minimal impact on the surrounding environment.

[0003] The circulating operating pressure is a key design parameter for evaluating the operational safety of compressed gas storage caverns. Among them, the upper limit internal pressure refers to the maximum gas pressure that the compressed gas storage cavern can withstand during operation. Once the internal pressure exceeds this threshold, it may cause excessive deformation of the surrounding rock, tensile failure, shear slip, or even lead to the overall uplift of the overlying strata, ultimately causing the gas storage facility to fail. The lower limit of internal pressure has a significant controlling effect on the structural fatigue response and plastic zone evolution under long-term cyclic internal pressure. Therefore, accurately calculating and determining the cyclic operating pressure range is crucial for ensuring the structural safety and airtightness of compressed gas energy storage caverns during up to 30 years and tens of thousands of injection-production cycles.

[0004] Existing methods for determining the ultimate internal pressure and cyclic operating pressure of underground compressed gas storage caverns still have significant limitations in their applicability to complex geological environments. Firstly, existing criteria primarily focus on preventing macroscopic damage induced by internal pressure, generally lacking effective utilization of geostress. Under deep burial conditions, initial geostress is a natural barrier maintaining the deformation coordination of the "surrounding rock-lining" composite structure. If the balance between internal pressure and initial geostress is ignored in the design, and geostress is not utilized to counteract the tensile effect generated by internal pressure, the lining structure design and reinforcement scheme will be conservative, increasing construction time and cost. Secondly, existing technologies highly focus on the static determination of the upper limit pressure, lacking a lower limit criterion for operating pressure based on fatigue damage and plastic zone evolution control in heterogeneous rock masses. Conventional methods often use static strength parameters, ignoring the fatigue decay of parameters such as rock mass cohesion and internal friction angle induced by high-frequency cyclic loading over an operating cycle of up to 30 years. Due to the lack of a unified method that can integrate the spatial heterogeneity of rock masses and dynamically solve the plastic zone expansion boundary after fatigue damage using efficient numerical algorithms, existing technologies struggle to scientifically define the lower limit internal pressure and the operating amplitude of cyclic pressure. In summary, existing methods cannot fully reflect the optimal stress state of underground compressed gas storage caverns under complex geological environments and long-term cyclic internal pressure. Therefore, there is an urgent need for a unified method for determining the operating pressure range that combines geostress balance constraints with dynamic fatigue damage correction, has clear physical meaning, and is easy to apply in engineering. Summary of the Invention

[0005] This invention aims to address the problems of existing technologies not fully considering the active constraint effect of geostress on the deformation of surrounding rock, and lacking quantitative control of fatigue damage of heterogeneous rock masses under cyclic loading. It provides a method for determining the operating pressure of compressed gas storage caverns using a dual constraint upper limit criterion and heterogeneous fatigue lower limit control.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a method for determining the operating pressure of a compressed air energy storage cavern, comprising the following steps: S1: Establish an elastic mechanical plane strain model of the surrounding rock-lining-sealing layer composite structure, and derive the analytical solutions of elastic stress and displacement of the surrounding rock-lining-sealing layer composite structure; S2: Based on the analytical solution of elastic stress and displacement, determine the upper limit of the cyclic internal pressure according to the first and second criteria. Among them, the first criterion is the displacement convergence criterion that controls the radial displacement of the inner surface of the sealing layer to be no greater than zero, and the second criterion is the tensile stress blocking criterion that controls the circumferential stress of the surrounding rock to be less than the tensile strength. S3: Introducing the spatial heterogeneity function of surrounding rock parameters, deriving the expressions for the elastoplastic stress and plastic zone radius of the surrounding rock-lining-sealing layer composite structure; S4: The fatigue damage evolution equation is introduced to correct the rock mass strength parameters. Based on the plastic zone radius control condition, the lower limit pressure is solved using the Newton-Raphson iterative method. .

[0007] This invention breaks through the limitations of traditional static design. It takes the active constraint effect of the initial geostress field on the deformation of the surrounding rock as the core, and establishes a displacement convergence criterion based on the radial displacement of the inner surface of the sealing layer not being greater than zero as the first criterion for the upper limit of internal pressure. It is supplemented by a tensile stress blocking criterion based on the circumferential stress of the surrounding rock being less than the tensile strength as the second criterion. At the same time, in view of the spatial heterogeneity of rock mass parameters and the parameter decay induced by long-term cyclic loading, it innovatively introduces spatial heterogeneity functions of the elastic modulus, cohesion and internal friction angle of the surrounding rock as a function of radial distance, as well as fatigue damage evolution equations for the decay of cohesion and internal friction angle with the number of cycles. Combined with the Newton-Raphson iterative solution based on the plastic zone radius control condition, a dynamic multi-criteria framework covering the dual constraint upper limit criterion and heterogeneous fatigue lower limit control is constructed. This method can simultaneously constrain the deformation of the surrounding rock by utilizing the initial geostress and quantify the decay of rock mass parameters caused by long-term cyclic loading. Under the premise of ensuring that the surrounding rock does not suffer tensile failure and that the expansion of the plastic zone is controllable, it can accurately quantify the optimal operating pressure range and amplitude of the compressed gas energy storage cavern over its entire life cycle of up to 30 years. This effectively optimizes design parameters and improves the economic efficiency of the project while ensuring the long-term sealing and safety of the structure.

[0008] Preferably, in step S1, the parameters obtained when establishing the elastic mechanical plane strain model include: the initial vertical stress of the surrounding rock. Lateral pressure coefficient Tunnel excavation radius Lining thickness Sealing layer thickness Elastic modulus of surrounding rock Poisson's ratio of surrounding rock lining elastic modulus Poisson's ratio of lining Elastic modulus of sealing layer and Poisson's ratio of the sealing layer The above parameters provide a complete input data foundation for subsequent analytical derivations, ensuring the accuracy and reliability of elastic stress and displacement calculations.

[0009] Preferably, in step S1, when deriving the analytical solutions for the elastic stress and displacement, the equilibrium equations, geometric equations, physical equations, and deformation compatibility equations are solved simultaneously to obtain the general solution for elastic displacement and stress in the polar coordinate system. Then, combining the interface boundary conditions and far-field stress boundary conditions of the surrounding rock-lining-sealing layer composite structure, the undetermined coefficients are solved to obtain the closed-form solutions for stress and displacement of the surrounding rock, lining, and sealing layer, respectively. Through the above analytical derivation method, rapid and accurate calculation of the mechanical response of the three-layer composite structure (surround rock, lining, and sealing layer) at any location can be achieved, providing a theoretical basis for determining the upper and lower limit pressures.

[0010] Preferably, in step S2, the upper limit of the cyclic internal pressure is determined. The specific steps are as follows: using the radial displacement of the inner surface of the sealing layer As the first criterion, the inverse solution yields the first upper limit internal pressure. The effective circumferential stress on the side of the surrounding rock at the interface between the surrounding rock and the lining. As the second criterion, among which The inverse solution yields the second upper limit internal pressure, representing the tensile strength of the surrounding rock. Take the smaller of the two values ​​as the upper limit of the loop pressure: The upper limit of the aforementioned cyclic internal pressure. The determination method can simultaneously ensure the safety of the cavern under the highest operating pressure from two physical levels: deformation constraint and strength constraint. It avoids the risk of cyclic cumulative failure caused by the reversal of the absolute displacement direction of the surrounding rock and lining, and prevents the generation of tension cracks in the surrounding rock.

[0011] Preferably, in step S3, the spatial heterogeneity function includes: the elastic modulus of the surrounding rock. Cohesion and internal friction angle Set about radial distance The spatial heterogeneity function can describe the geological characteristics of surrounding rock properties that change continuously with spatial location or are distributed in layers. It avoids the calculation bias that may be introduced by traditional homogeneous models due to neglecting the spatial variability of rock masses, and helps to improve the reliability of the calculation results of plastic zone radius and lower limit pressure.

[0012] Preferably, in step S3, when deriving the expressions for the elastoplastic stress and the radius of the plastic zone, based on the assumption that the principal stress direction of the plastic zone of the surrounding rock is consistent with the elastic state, the expressions for the radial stress, circumferential stress, and radius of the plastic zone of the surrounding rock are obtained by simultaneously solving the equilibrium equations, the Mohr-Coulomb criterion, and the boundary conditions as follows: , , , in, For radial stress in the plastic zone of the surrounding rock, For the circumferential stress in the plastic zone of the surrounding rock, The radius of the plastic zone of the surrounding rock. Radial stress at the elastoplastic interface For the cohesion of the surrounding rock, Let be the internal friction angle of the surrounding rock. The expression obtained by the above method can quantitatively describe the stress redistribution characteristics and the expansion range of the plastic zone after the surrounding rock enters the plastic state, providing an analytical basis for subsequently using the plastic zone radius control condition to back-calculate the lower limit pressure.

[0013] Preferably, in step S4, the fatigue damage evolution equation is: , , in, The number of loops. and These represent the cohesion and internal friction angle of the surrounding rock, respectively. and These are fatigue damage evolution functions for cohesion and internal friction angle, respectively. The fatigue damage evolution equation is specifically in logarithmic form: , , in, and These are parameters obtained by fitting from cyclic fatigue mechanical tests.

[0014] By introducing the fatigue damage evolution equations that describe the decay of cohesion and internal friction angle with the number of cycles, and specifically using logarithmic form to describe this decay law, we can quantify the cumulative weakening effect of tens of thousands of injection and production cycles over 30 years on the rock mass strength parameters. This ensures that the determined lower limit pressure still has sufficient safety reserves at the end of the power plant's operation, and reduces the risk of sudden instability that may be caused by the decay of rock mass parameters over time.

[0015] Preferably, in step S4, the control condition for the radius of the plastic zone is: the increase in the radius of the plastic zone of the surrounding rock under cyclic internal pressure relative to the plastic radius induced by tunnel excavation does not exceed 5%. This control condition for the radius of the plastic zone provides a clear physical criterion for determining the lower limit pressure, allowing the surrounding rock to undergo limited plastic deformation under operating pressure to exert its self-bearing capacity, while strictly controlling the excessive expansion of the plastic zone, thus balancing structural safety and material utilization efficiency.

[0016] Preferably, in step S4, the Newton-Raphson iterative method is used to solve for the lower limit pressure. The iterative formula is: , in, Current internal pressure The residual function value under the following conditions For residual function Pressure inside the tunnel The first derivative of the gas storage pressure is used to determine the minimum internal pressure required to maintain the plastic zone from expanding, which is then determined as the lower limit pressure. By employing the Newton-Raphson iterative method to solve the nonlinear function relating the maximum allowable plastic zone radius and the current internal pressure, the minimum gas storage internal pressure level required to maintain the plastic zone from expanding can be calculated efficiently and accurately. This solves the computational problem of directly solving the lower limit pressure using conventional analytical methods under conditions of discontinuous variation in heterogeneous rock mass parameters, ensuring rapid convergence of the iterative process and the scientific validity of the calculation results.

[0017] Preferably, step S5 is also included: based on the determined operating pressure range. Multi-cycle loading and unloading numerical simulations were conducted to verify the operational safety of the compressed gas energy storage cavern throughout its entire life cycle. This step, based on theoretical analysis results, further considers complex non-uniform geological conditions and nonlinear material behavior, verifying the safety margin of the operating pressure range from a numerical calculation perspective, and providing a basis for formulating an optimized operating pressure scheme suitable for engineering applications.

[0018] Compared with the prior art, the present invention has the following advantages: (1) An innovative upper limit criterion based on active geostress constraint is proposed: taking the active constraint effect of the initial geostress field on the deformation of the surrounding rock as the core, an innovative displacement convergence criterion based on the radial displacement of the inner surface of the sealing layer not being greater than zero ("absolute displacement ≤ 0" criterion) is proposed. By utilizing the geostress to force both the absolute deformation of the lining and the surrounding rock to exhibit an "inward convergence" state, the risk of cyclic cumulative failure caused by the reversal of the absolute displacement direction of the surrounding rock and lining is eliminated from the physical mechanism. At the same time, a tensile stress blocking criterion is used to ensure that the surrounding rock does not undergo tensile failure by using the circumferential stress of the surrounding rock being less than the tensile strength. By jointly determining the upper limit of internal pressure through dual constraints, the limitation of traditional static design that only focuses on macroscopic failure is broken.

[0019] (2) Accurate handling of geological complexity and long-term fatigue decay: In view of the spatial heterogeneity of rock mass parameters and the parameter decay induced by long-term cyclic load, the spatial heterogeneity function of the elastic modulus, cohesion and internal friction angle of the surrounding rock as a function of radial distance is innovatively introduced, and the radius of the plastic zone under heterogeneous rock mass conditions is solved by the Newton-Raphson iterative algorithm. Compared with the traditional homogeneous model, it can more accurately capture the sensitivity of the cyclic operating pressure amplitude to the expansion of the plastic zone. At the same time, the fatigue damage evolution equation of the cohesion and internal friction angle decaying with the number of cycles is explicitly introduced to ensure that the obtained operating pressure range still has sufficient safety reserves at the end of the 30-year operation of the power station, effectively avoiding the risk of sudden instability caused by the decay of rock mass parameters over time.

[0020] (3) Achieve precise quantification of the operating pressure range throughout the entire life cycle: By constructing a dynamic multi-criteria framework that includes the upper limit criterion of dual constraints and the lower limit control of heterogeneous fatigue, this method can, under the premise of ensuring that the surrounding rock does not suffer tensile failure and the expansion of the plastic zone is controllable, simultaneously constrain the deformation of the surrounding rock by initial geostress and quantify the decay of rock mass parameters caused by long-term cyclic loads, achieve precise quantification of the optimal operating pressure range and amplitude of the compressed gas energy storage cavern throughout its entire life cycle of up to 30 years. This effectively optimizes design parameters and improves engineering economy while ensuring the long-term sealing and safety of the structure. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the method for determining the operating pressure of a compressed air energy storage cavern in the embodiment; Figure 2 This is a schematic diagram of the elastic mechanical plane strain model of the surrounding rock-lining-sealing layer composite structure established in the embodiment; Figure 2 The specific reference numerals in the attached figures are as follows: ①- Initial vertical stress of surrounding rock ②-Horizontal ground stress ③ - Tunnel excavation radius ④ - Polar coordinate angle θ; ⑤ - Surrounding rock; ⑥ - Lining; ⑦ - Sealing layer. Detailed Implementation

[0022] Example: The operating pressure of a deep, hard rock circular gas storage cavity is determined using the method of this invention. Figure 1 As shown, the specific process of this method is as follows: Phase 1 – Acquisition of in-situ in-situ stress and rock mass engineering parameters: Establish an elastic mechanical plane strain model for the surrounding rock-lining-sealing layer composite structure, such as... Figure 2 As shown. Based on the preliminary site selection and design of the compressed air energy storage project, the excavation radius of the gas storage cavern was obtained through geological exploration, in-situ stress testing, indoor rock sample testing, and engineering classification evaluation. Initial vertical stress of surrounding rock Lateral pressure coefficient Elastic modulus of surrounding rock Poisson's ratio of surrounding rock Based on the engineering design data, the preliminary lining thickness is determined. Sealing layer thickness lining elastic modulus Poisson's ratio of lining Elastic modulus of sealing layer and Poisson's ratio of the sealing layer .

[0023] Phase Two – Characterization and Parameter Determination of Surrounding Rock Heterogeneity: Based on the rock mass strength and deformation parameters obtained from the tests, the elastic modulus of the surrounding rock is... Cohesion and internal friction angle Set about radial distance The function of . In this embodiment, it is assumed that the elastic modulus of the surrounding rock varies with the radius of the gas storage cavern as the origin. Change, following the formula Give the non-uniformity coefficient Possible values ​​for . Based on engineering design data, obtain the lining thickness. Sealing layer thickness lining elastic modulus Poisson's ratio of lining Elastic modulus of sealing layer and Poisson's ratio of the sealing layer .

[0024] Phase 3 – Calculating the Upper Limit of Cyclic Pressure : This stage, based on the plane strain model of elasticity, simultaneously solves the equilibrium equations, geometric equations, physical equations, and deformation compatibility equations to obtain the general solution for displacement and stress in the polar coordinate system. Then, combining the interface boundary conditions and far-field stress boundary conditions of the surrounding rock-lining-sealing layer composite structure, it solves for the undetermined coefficients, obtaining the closed-form solutions for stress and displacement of the surrounding rock, lining, and sealing layer. Based on this, the upper limit of the cyclic internal pressure is determined according to the following steps: The first step is displacement control. To ensure that the deformation caused by operating pressure does not exceed the constraint force of the initial ground stress, the radial displacement of the inner surface of the sealing layer is controlled. As the first criterion (i.e., the absolute displacement convergence (zero expansion) criterion), the relevant parameters of the in-situ stress and the surrounding rock-lining-sealing layer are substituted into the plane strain model of elasticity, and the first upper limit internal pressure is obtained by inverse solution. ; The second step is strength control (tensile strength criterion). This is based on the effective circumferential stress on the surrounding rock side at the interface between the surrounding rock and the lining. As the second criterion (i.e., the surrounding rock circumferential tensile stress blocking criterion), The inverse solution yields the second upper limit internal pressure, representing the tensile strength of the surrounding rock. ; Step 3: Take the smaller of the two upper limit internal pressures mentioned above as the upper limit of the circulating internal pressure of the gas storage chamber: .

[0025] Fourth stage – Determining the lower limit pressure based on heterogeneous fatigue iteration : This stage first performs an approximate analytical analysis of the elastoplastic properties of the heterogeneous rock mass. Specifically, based on the assumption that the principal stress direction in the plastic zone of the surrounding rock is consistent with the elastic state, the radial stress in the plastic zone of the surrounding rock is obtained by simultaneously applying the equilibrium equations, the Mohr-Coulomb criterion, and the boundary conditions. Circumferential stress and radius of the plastic zone The expression is as follows: , , , in, For radial stress in the plastic zone of the surrounding rock, For the circumferential stress in the plastic zone of the surrounding rock, The radius of the plastic zone of the surrounding rock. Radial stress at the elastoplastic interface For the cohesion of the surrounding rock, It is the internal friction angle of the surrounding rock.

[0026] Then, the fatigue damage evolution equation is introduced to correct the rock mass strength parameters. The number of cycles N corresponding to the design life (e.g., 30 years) is set; in this embodiment, N = 10000 cycles. Based on the lithology of the surrounding rock at the location of the gas storage cavern, cyclic fatigue mechanical tests are conducted, and the relationship between the strength parameters of the surrounding rock and the number of cycles is obtained by fitting the equations. , , in, and These are parameters obtained by fitting from cyclic fatigue mechanical tests.

[0027] Next, a set of nonlinear equations for the heterogeneous plastic zone is constructed. The maximum allowable plastic zone radius is defined as the increase in the radius of the plastic zone of the surrounding rock under cyclic internal pressure relative to the plastic radius induced by tunnel excavation, which is no more than 5%. The control conditions. First, calculate the cavern pressure. Radius of the plastic zone of the surrounding rock Give the maximum allowable plastic zone radius under the condition of internal pressure in the cavity. Substituting the above fatigue damage evolution equation into the expression for the radius of the plastic zone of the surrounding rock, the radius of the plastic zone when there is internal pressure in the tunnel is obtained. Based on this, the lower limit internal pressure residual function is defined. .

[0028] Finally, the lower limit pressure was solved using the Newton-Raphson iterative method. Through adaptive iterative convergence, the minimum internal gas pressure required to prevent the expansion of the plastic zone under fatigue damage conditions is accurately determined and identified as the lower limit pressure. The iterative formula is: , in, Current internal pressure The residual function value under the following conditions For residual function Pressure inside the tunnel The first derivative. Based on the lower limit internal pressure residual function. Solve The root is the lower limit pressure. The specific solution steps are as follows: Step 1: Guess the initial value of the lower limit internal pressure ; Step 2: Calculate the residual function value and its derivative ; Step 3: Update the internal pressure according to the Newton-Raphson iterative formula. ; Step 4: Determine the convergence condition If this criterion is met, then This serves as the minimum internal gas pressure required to control the radius of the plastic zone to not exceed the maximum allowable value under fatigue damage conditions.

[0029] Phase 5 – Full Life Cycle Numerical Simulation Verification: Based on the determined operating pressure range Multi-cycle loading and unloading numerical simulation calculations were carried out. In this embodiment, commercial numerical simulation software was used to verify the long-term operational safety of the gas storage cavern over 30 years, and finally an optimized operating pressure scheme was formed.

[0030] Phase 6 – Application of Engineering Parameter Back-Depth: This invention not only introduces a fatigue damage evolution equation to correct rock mass strength parameters, but also utilizes Newton-Raphson iteration to accurately solve the calculation problem of discontinuous changes in heterogeneous rock mass parameters, ensuring the scientific validity of the calculation results. In the practical application of compressed air energy storage projects, the operating pressure and amplitude of the storage cavern are generally determined by a combination of factors, including grid power generation and energy storage system capacity. To ensure the underground storage cavern can operate safely for 30 years, key parameters such as the cavern's burial depth and the orientation between the cavern's axial direction and the direction of maximum horizontal ground stress can be deduced from the determined upper and lower limits of the operating pressure. This method is also applicable to the site selection and preliminary design of supporting storage caverns.

Claims

1. A method for determining the operating pressure of a compressed air energy storage cavern, characterized in that, Includes the following steps: S1: Establish an elastic mechanical plane strain model of the surrounding rock-lining-sealing layer composite structure, and derive the analytical solutions of elastic stress and displacement of the surrounding rock-lining-sealing layer composite structure; S2: Based on the analytical solution of elastic stress and displacement, determine the upper limit of the cyclic internal pressure according to the first and second criteria. Among them, the first criterion is the displacement convergence criterion that controls the radial displacement of the inner surface of the sealing layer to be no greater than zero, and the second criterion is the tensile stress blocking criterion that controls the circumferential stress of the surrounding rock to be less than the tensile strength. S3: Introducing the spatial heterogeneity function of surrounding rock parameters, deriving the expressions for the elastoplastic stress and plastic zone radius of the surrounding rock-lining-sealing layer composite structure; S4: The fatigue damage evolution equation is introduced to correct the rock mass strength parameters. Based on the plastic zone radius control condition, the lower limit pressure is solved using the Newton-Raphson iterative method. .

2. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S1, the parameters obtained when establishing the elastic mechanical plane strain model include: the initial vertical stress of the surrounding rock. Lateral pressure coefficient Tunnel excavation radius Lining thickness Sealing layer thickness Elastic modulus of surrounding rock Poisson's ratio of surrounding rock lining elastic modulus Poisson's ratio of lining Elastic modulus of sealing layer and Poisson's ratio of the sealing layer .

3. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S1, when deriving the analytical solutions for elastic stress and displacement, the equilibrium equations, geometric equations, physical equations, and deformation compatibility equations are solved simultaneously to obtain the general solution for elastic displacement and stress in the polar coordinate system. Then, the interface boundary conditions and the far-field stress boundary conditions of the surrounding rock-lining-sealing layer composite structure are combined to solve for the undetermined coefficients and obtain the closed-form solutions for stress and displacement of the surrounding rock, lining, and sealing layer, respectively.

4. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S2, the upper limit of the cyclic internal pressure is determined. The specific steps are as follows: using the radial displacement of the inner surface of the sealing layer As the first criterion, the inverse solution yields the first upper limit internal pressure. The effective circumferential stress on the side of the surrounding rock at the interface between the surrounding rock and the lining. As the second criterion, among which The inverse solution yields the second upper limit internal pressure, representing the tensile strength of the surrounding rock. Take the smaller of the two values ​​as the upper limit of the loop pressure: .

5. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S3, the spatial heterogeneity function includes: the elastic modulus of the surrounding rock. Cohesion and internal friction angle Set about radial distance The function.

6. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S3, when deriving the expressions for the elastoplastic stress and the radius of the plastic zone, based on the assumption that the principal stress direction of the plastic zone of the surrounding rock is consistent with the elastic state, the expressions for the radial stress, circumferential stress, and radius of the plastic zone of the surrounding rock are obtained by simultaneously solving the equilibrium equations, the Mohr-Coulomb criterion, and the boundary conditions: ， ， ， in, For radial stress in the plastic zone of the surrounding rock, For the circumferential stress in the plastic zone of the surrounding rock, The radius of the plastic zone of the surrounding rock. Radial stress at the elastoplastic interface For the cohesion of the surrounding rock, It is the internal friction angle of the surrounding rock.

7. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S4, the fatigue damage evolution equation is: ， ， in, The number of loops. and These represent the cohesion and internal friction angle of the surrounding rock, respectively. and These are fatigue damage evolution functions for cohesion and internal friction angle, respectively. The fatigue damage evolution equation is specifically in logarithmic form: ， ， in, and These are parameters obtained by fitting from cyclic fatigue mechanical tests.

8. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S4, the control condition for the radius of the plastic zone is: the increase in the radius of the plastic zone of the surrounding rock under cyclic internal pressure relative to the plastic radius induced by the excavation of the tunnel does not exceed 5%.

9. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, In step S4, the lower limit pressure is solved using the Newton-Raphson iterative method. The iterative formula is: ， in, Current internal pressure The residual function value under the following conditions For residual function Pressure inside the tunnel The first derivative of the gas storage pressure is used to determine the minimum internal pressure required to maintain the plastic zone from expanding, which is then determined as the lower limit pressure. .

10. The method for determining the operating pressure of a compressed air energy storage cavern according to claim 1, characterized in that, It also includes step S5: based on the determined operating pressure range We conducted multi-cycle loading and unloading numerical simulations to verify the operational safety of the compressed gas energy storage cavern throughout its entire life cycle.

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