A conventional constant-volume compressed air energy storage system (CAES) is integrated with a constant-pressure configuration to propose an underground CAES system employing a staged multi-level compression strategy. A comprehensive thermodynamic model is developed encompassing the surface compression units, heat exchangers, expansion turbines, and the subterranean storage cavern. Moreover, a fully coupled simulation framework is implemented in COMSOL Multiphysics to capture the combined thermodynamic response of both surface equipment and the underground cavern throughout charge-discharge cycles. Results indicate that the proposed constant-pressure CAES exhibits distinctive compression and expansion behavior compared with traditional CAES, particularly in terms of compressor power, air thermal evolution, and turbine performance. Parametric studies further reveal that operational parameters, such as charging rate, heat exchanger efficiency, and hydrostatic pressure, substantially affect energy consumption, discharge capability, and overall round-trip efficiency. These insights elucidate the thermodynamic characteristics and key performance drivers of the system, offering guidance for its parameters optimization.

Compressed Air Energy Storage (CAES) systems have emerged as a critical research focus in the field of energy storage due to their long-duration and high-efficiency storage capabilities. The structural stability of underground air storage caverns is governed by the combined effects of non-hydrostatic initial in-situ stress fields and cyclic internal air pressure. However, existing studies often rely on simplified geological models or static analysis methods, lacking a unified theoretical framework for analyzing long-term dynamic elastoplastic behavior, which limits effective guidance for optimizing cavern layout design. To address this gap, this paper establishes a comprehensive analytical framework integrating the Muskhelishvili complex variable function method and the Melan’s shakedown theorem. First, closed-form solutions for the stress-displacement field of the surrounding rock under elastic conditions are derived. Subsequently, based on the Melan’s shakedown lower-bound theorem, assuming that the principal stress directions in the plastic zone align with those in the elastic state, an approximate analytical formula for the maximum allowable cyclic internal pressure amplitude to maintain the dynamic shakedown state of the cavern is derived, with its rationality and accuracy validated through numerical simulations. Parametric sensitivity analysis reveals that cavern depth, lateral pressure coefficient, and internal air pressure are the primary factors influencing both static stability and dynamic shakedown, while excavation radius and lining thickness are secondary factors. Furthermore, this study proposes the in-situ stress-to-internal pressure ratio as a dimensionless evaluation metric for optimizing cavern layout design. It is found that a high in-situ stress-to-internal pressure ratio combined with a larger lateral pressure coefficient significantly enhances the overall stability of underground air storage caverns and effectively suppresses cumulative plastic deformation. However, when internal pressure is low, an excessively high in-situ stress-to-internal pressure ratio and lateral pressure coefficient may increase the risk of plastic yielding in the surrounding rock and lining. The findings provide theoretical and practical guidance for the safe design and optimization of underground CAES caverns. Future research should incorporate field experiments to further clarify the applicable range and engineering reliability of the in-situ stress-to-internal pressure ratio, refining the theoretical framework and promoting practical engineering applications.

Large-scale energy storage is key to supporting high proportions of renewable energy and ensuring stable grid operation. Given the volume requirements of megawatt-scale energy storage power stations, underground cavern clusters are the obvious choice. However, theoretical modeling of cavern clusters under complex boundary conditions remains challenging, especially when considering uniform radial internal pressure and non-uniform reaction forces from adjacent caverns, which are difficult to solve using existing analytical methods. To this end, this paper proposes a boundary compensation analytical method based on the Schwarz alternating iteration idea. By modifying the Laurent series and combining it with the Taylor–Fourier expansion, Python programming is used to achieve efficient and automated solution of the cavern boundary matching and analytical model. Furthermore, the dimensionless vertical stress–cavern internal pressure ratio η parameter is introduced to analyze the stress response of rock pillars under synchronous and asynchronous operating conditions. The results show that the first iteration of the internal boundary residual can converge to the order of 10^-2 , and the correctness of this method is verified by a single-cavern degradation example. The stress in the middle rock pillars is controlled by the superposition of horizontal and vertical stresses. The introduced vertical stress–cavern internal pressure ratio ( η ) can uniformly characterize the stress evolution law under different internal pressure conditions. Under synchronous and asynchronous operating conditions, the η value and lateral pressure coefficient jointly determine the stress state of the rock pillars and its evolution. Based on the η parameter, an optimization criterion for the layout of energy storage cavern clusters was proposed, and its engineering applicability was verified through calculation examples. The method proposed in this paper breaks through the limitations of traditional analysis, which is difficult to handle complex superimposed boundaries, and provides a generalizable theoretical framework for the analysis of underground energy storage multi-cavern clusters.

In this study, cyclic air injection–withdrawal model tests were conducted using a large-scale physical model system to investigate the long-term deformation characteristics of the rock mass. Based on the experimental observations, a spatiotemporal evolution equation of deformation was established, and an equivalent deformation modulus approach was proposed to characterize the long-term deformation effect. By embedding this evolution law into a multi-field coupled framework, a numerical solution method considering long-term deformation of rock mass was developed. The results indicate that the rock mass exhibits pronounced spatiotemporal evolution characteristics under cyclic internal pressure. Temporally, deformation shows an exponential-type growth with asymptotic stabilization, accompanied by significant accumulation of residual deformation. Spatially, the influence of cyclic pressure attenuates rapidly with radial distance and becomes negligible beyond approximately three times the cavern radius. The proposed model effectively captures the evolution of structural mechanical responses, including cavern displacement and stresses in the steel liner and reinforcement. Thermodynamic effects lead to variations of approximately 13

Based on the Hoek-Brown strength criterion,this study develops a semi analytical approach for calculating the stress and displacement of surrounding rock throughout the excavation and high-pressure operation stages of a compressed gas energy storage cavern,thereby elucidating the evolution patterns of the stress path and failure mode in the surrounding rock.The findings reveal that the geological parameters exert minimal influence on the distribution of radial stresses within the surrounding rock,and significantly affect the distribution of circumferential stresses.Poorer geological conditions lead to a larger circumferential stress and a wider plastic zone.For medium-soft rock formations(e.g.geological strength index GSI=35),the Mohr-Coulomb strength criterion may overestimate the bearing capacity of surrounding rock during high-pressure air storage stage.Should the surrounding rock transition into a plastic state during cavern excavation,it will be subjected to both radial and circumferential compression under conditions of high internal gas pressure.As the internal gas pressure escalates,the stress state of the surrounding rock sequentially progresses through plastic unloading,plastic loading,and plastic expansion stages.Notably,the critical internal pressure threshold during the plastic expansion stage is roughly twice the initial in-situ stress.Once the internal gas pressure reaches this critical pressure,the radius of the plastic zone in the surrounding rock expands almost linearly with the internal pressure,resulting in a swift enlargement of the plastic zone and a nonlinear surge in the displacement of the surrounding rock.Consequently,under unfavorable geological conditions,it is inadvisable to indiscriminately elevate the maximum gas storage pressure within the cavern.

Spatial variability in mechanical properties significantly affects fracture evolution in materials. A strict random phase field model suitable for spatially heterogeneous materials is developed, in which a gradient term of the critical energy release rate is introduced. Compared with the simple integration of traditional finite element models with random fields, which involves merely replacing deterministic mechanical properties in the governing equations, a more accurate coupling approach is adopted by incorporating a coordinate-dependent critical energy release rate into the energy functional, which is reformulated from existing models. The governing equation of the phase field is derived through variational principles. Unlike traditional random phase field models, the proposed model captures the spatial variation in the gradient of the critical energy release rate and effectively characterizes the directional rate of change in fracture toughness. The proposed model is implemented by using COMSOL Multiphysics and MATLAB, and validated through the rock fracture experiment. Quasi-static and dynamic fracture simulations reveal that in the presence of pronounced spatial heterogeneity, incorporating the critical energy release rate gradient can significantly alters fracture behavior in heterogeneous materials, often producing effects not captured by traditional random phase field models. Therefore, the rigorous random phase field model is indispensable for understanding and predicting the fracture behavior of spatially heterogeneous materials such as rocks.

Monolithic cast concrete linings in underground energy storage caverns with high internal pressure are prone to cracking, which compromises the structural stability and integrity of the sealing layer. To mitigate this problem, previous studies proposed implementing preset seams within the lining to release circumferential deformation. However, under high internal pressure, significant shear stress still develops along the outer boundary of the concrete lining, leading to severe tensile damage in the central portion of the lining. To address this issue, this study proposes a composite segmented lining system incorporating a sliding layer. In this system, a sliding layer is implemented at the outer boundary of the segmented lining, reducing the shear stiffness and thus lowering the shear stress, while further enhancing the deformation release capacity of the segmented lining. Based on sliding-layer mechanical tests and numerical analyses, this study investigates the influence of interfacial shear stiffness and the number of preset seams on the mechanical response of the lining and the surrounding rock. The analysis explicitly accounts for the interaction between the lining and the surrounding rock. The results indicate that when the interfacial shear stiffness is high, increasing the number of preset seams has only a limited influence on the stress state of the lining. Only under low interfacial shear stiffness can additional preset seams effectively release the deformation and reduce the structural stress of the lining. Moreover, since an excessive number of preset seams may compromise the structural integrity of the lining, reducing the interfacial shear stiffness is a more effective optimization strategy than further increasing the number of preset seams for alleviating lining stresses. The findings further show that decreasing the interfacial shear stiffness can substantially reduce the number of preset seams required, thereby maintaining the overall structural integrity of the lining while mitigating its stress. This study provides a theoretical basis for optimizing the lining design of underground energy storage caverns.

A large-scale physical model test system for underground lined rock caverns of compressed air energy storage (CAES) is independently developed. This testing system consists of four subsystems: a hydraulic loading system, an automatic cycling gas charging and discharging system, an air sealing system, and a data acquisition and monitoring system. The developed physical model system can simulate the coupling of physical processes, such as stress, temperature, and air flow, and can reproduce the actual operational process of a CAES cavern to the maximum extent. With this physical model test system, a cycling gas charging and discharging test of CAES caverns is conducted. The model test reveals the thermodynamic response of air and the mechanical response characteristics of the surrounding rock and lining during the CAES cycles. The model test shows the cumulative deformation behavior of the surrounding rock under cyclic internal pressure confirms the suitability and reliability of the sealing layer.

Existing analytical solutions for compressed air energy storage (CAES) caverns commonly assume the concrete lining to be elastic or elastoplastic, which may overestimate its load-bearing capacity by neglecting cracking-induced stiffness degradation. To address this limitation, this study develops an iterative elastoplastic analytical solution for CAES underground caverns by explicitly incorporating the non-uniform radial and hoop damage characteristics of the concrete lining under high internal pressure. A coupled iterative solution strategy is proposed to efficiently solve the resulting nonlinear formulation. The proposed model is validated against numerical simulations for a CAES cavern project currently under construction, showing excellent agreement while achieving significantly improved computational efficiency. The results indicate that the structural behavior of the CAES cavern is highly sensitive to cavern size, operating pressure, steel liner thickness, and particularly the quality of the host rock, whereas variations in concrete lining thickness produce only a minor effect. In addition, the load-transfer relationship among different structural components is mainly controlled by geometric configuration and material properties, while exhibiting limited sensitivity to the applied air pressure magnitude. These findings indicate that explicitly accounting for lining damage is essential for accurately evaluating the mechanical behavior of CAES caverns. The proposed analytical framework provides both improved prediction accuracy and high computational efficiency, making it a practical tool for engineering design and parametric analysis.

Conventional reinforced concrete linings in underground compressed air energy storage (CAES) caverns located in poor rock conditions are prone to cracking due to insufficient deformation capacity. Such cracking causes the flexible sealing layer to be entrapped into the cracks, resulting in its mechanical failure and consequent loss of sealing integrity. To address this issue, this paper proposes a composite lining comprising an inner high-strength engineered geopolymer composite (EGC) layer and an outer fiber-reinforced polymer (FRP) reinforced concrete backing layer. This design leverages the high deformation capacity, crack control capability, and durability of the composite lining to extend the applicability of CAES to regions with poor rock mass conditions. Through material mechanical tests, the mechanical properties of EGC under cyclic loading were characterized, and the influence of thickness effect was examined. Based on the test results, a cyclic constitutive model for EGC was developed within the concrete damaged plasticity (CDP) framework in ABAQUS. A two-dimensional finite element model of underground CAES cavern with the composite lining was then established. The long-term mechanical responses of the lining and surrounding rock were systematically simulated under single and 10,000 cycles loading, and the effects of EGC layer thickness and internal pressure amplitude ratio were analyzed. The results indicate that, under Class IV poor rock conditions, the maximum tensile stress in the EGC layer of the composite lining after a single gas storage cycle is 3.97 MPa, which remains below its cracking strength. After 10,000 cycles, the maximum tensile stress increases to 4.47 MPa. Although cracking occurs in the EGC layer under this stress, the crack width remains far smaller than the code limit. The tensile stress in the FRP bars stays far below their tensile strength. The deformation of the surrounding rock remains essentially stable. Increasing the EGC layer thickness reduces its maximum tensile stress and decreases the deformation variation in the surrounding rock. A higher internal pressure amplitude ratio is beneficial to the stability of the surrounding rock. Overall, the proposed composite lining demonstrates favorable stability and safety under long-term cyclic loading.

An analytical formulation derived from the Burgers viscoelastic model was developed to characterize the long-term deformation of the host rock. Then, long-term storage model tests were carried out using a multi-functional apparatus designed for high-pressure underground caverns, and the rheological parameters of the host rock were identified using experimental data and particle swarm optimization (PSO) with a correlation coefficient of major monitoring points exceeding 0.97. Results indicate a gradual increase in the radial strain of the host rock over time, with more pronounced rheological characteristics near the cavern wall. The proposed Burgers-based analytical model accurately reproduces the observed creep response, in which the radial displacement at the inner wall exhibits an initial nonlinear growth followed by a steady linear evolution. Importantly, this study establishes an integrated workflow combining physical model testing, analytical modeling, and parameter identification for CAES caverns, which enables the quantification of creep effects under realistic operational conditions. The findings provide novel scientific insights into the time-dependent mechanical behavior of the host rock and demonstrate the significant impact of rock creep on cavern structural response. Furthermore, from an engineering perspective, the proposed methodology offers a reproducible framework for incorporating long-term creep effects into the design and safety assessment of CAES caverns, highlighting potential underestimation of deformation and structural demand when relying solely on maximum internal pressure.

Based on the Hoek-Brown strength criterion, a novel semi-analytical solution was proposed to characterize the mechanical response of surrounding rock in compressed air energy storage caverns operating in high internal pressure considering its bidirectional strain-softening characteristics. The stress path and strain-softening characteristics of the surrounding rock from the excavation stage to the gas storage stage under high internal pressure were systematically explored. The influence of softening degree on the stress path of the surrounding rock was investigated. Results indicate that, when the initial geostress is high or the surrounding rock strength is low, a plastic zone forms immediately after excavation. As internal pressure increases, the surrounding rock sequentially undergoes plastic unloading, plastic loading, and plastic expansion stages. The relationship between stress in the plastic zone and rock strength remains an active area of research. In contrast to scenarios that disregard strain-softening, the incorporation of strain-softening results in substantially divergent stress curve profiles. During the excavation process, the circumferential stress within the plastic zone undergoes a decrease. Meanwhile, under conditions of high-pressure gas storage, it experiences an increase. Strain-softening has been shown to significantly increase surrounding rock displacement and substantially expand the plastic zone. The rate of plastic zone radius growth accelerates during the plastic expansion stage. When the surrounding rock is substandard, strain-softening considerably increases the displacement of the surrounding rock and the extent of the plastic zone. These changes exert a more substantial influence on the tensile stress experienced by the lining under high internal pressure and its design sensitivity. The analytical approach proposed in this study extends traditional stress path analysis methods that neglect strain-softening. The findings provide theoretical support and new insights for the mechanical calculation and structural design of surrounding rock in underground caverns subjected to high internal pressure within medium-quality or soft rock masses.

Compressed air energy storage (CAES) tunnels undergo daily inflation and deflation cycles during operation. It is inevitable that the surrounding rock will undergo fatigue damage when subjected to long-term cyclic loading. This damage leads to cumulative plastic deformation and a reduction in bearing capacity. Based on the Mohr-Coulomb criterion incorporating fatigue damage and stress path theory, this study presents an analytical solution for the mechanical response of surrounding rock during tunnel excavation, initial inflation, initial deflation, and cyclic inflation-deflation. The findings of the study suggest that the minimum air storage pressure, herein referred to as qmin, exerts a significant influence on the mechanical response of the surrounding rock. In circumstances where the qmin is elevated (7.5 MPa), the surrounding rock transitions into a stable cyclic stage of plastic unloading-reloading, characterized by the formation of closed stress paths. Conversely, when qmin decreases to 1.5 MPa, the substantial pressure differential engenders a plastic reloading state during the process of deflation. The stress path subsequently becomes non-closed and gradually shifts toward strength degradation with increasing cycle numbers, accelerating cumulative plastic deformation and reducing load-bearing capacity. Damage parameters exert a staged influence on mechanical behavior: during air storage, they intensify circumferential stress concentration and increase displacement; during deflation, they amplify stress fluctuations and rebound deformation. These findings provide a theoretical basis for determining the operational pressure range and assessing the long-term stability of rock tunnels.

An analytical stress calculation method of rock caverns for compressed air energy storage (CAES) with nonhydrostatic initial ground stress under the full bonding contact and Coulomb frictional contact between lining and surrounding rock is proposed, respectively. In the solutions, a displacement release coefficient 7 is introduced to consider the support delay during the construction stage, and the superposition method is adopted to consider the thermal strain during the operational stage. Moreover, the solution under the full bonding contact condition is established through the complex function theory with power series method. In addition to this method, the optimization method is also utilized to derive the solution of the Coulomb frictional contact. Numerical simulations are carried out to validate the proposed stress solutions. Finally, the stress distribution and load transfer of rock caverns are discussed based on a case study with various influencing factors. Results demonstrate that the contact condition possesses a significant influence on the stress of lining, but has weak effect on the stress in surrounding rock. The stress in lining under the Coulomb frictional contact is less than that of full bonding contact. Especially, the circumferential tensile stress in lining is significantly reduced under the frictional contact. The load transfer ratio xi, defined as the load of high internal air pressure transferred from the lining to the surrounding rock, rises as the elastic modulus ratio rE of surrounding rock to lining increases. Increasing rE is an effective way to control the circumferential tensile stress of lining resulted from high internal air pressure. With the same rE, xi under Coulomb frictional contact keeps higher than that of full bonding contact. As 7 increases, xi gradually decreases, and xi rises with increasing initial ground stress.

The steel lining is a critical structural component in high-pressure tunnels, serving not only as a sealing barrier but also as a load-bearing element that resists a portion of the internal pressure. Its mechanical performance directly influences the operational safety of the tunnel. However, under conditions such as weak surrounding rock, conventional sealing designs based on elastic assumptions often require excessively large lining thicknesses, leading to increased construction costs and an underutilization of the load-bearing capacity of the surrounding rock. To address these limitations, this study introduces a controlled-yielding design of the steel lining. An elastoplastic analytical solution that incorporates the yielding behavior of the steel lining and its interaction with the surrounding rock is developed, enabling a systematic characterization of their mechanical responses during the plastic stage. The results demonstrate that the controlled-yielding design exhibits pronounced advantages under weak surrounding rock conditions, allowing a substantial increase in the ultimate internal pressure capacity of the cavern without increasing the lining thickness. Moreover, under a given internal pressure, the controlled-yielding design can markedly reduce the required thickness of the steel lining. After the steel lining yields, the contact pressure becomes constant as it is governed by the yielding criterion, meaning that the lining's load-bearing contribution no longer increases even when the surrounding rock becomes weaker. Consequently, the load-sharing ratio of the surrounding rock increases significantly under weak rock conditions, allowing its bearing capacity to be fully mobilized. Overall, the proposed controlled-yielding design of the steel lining provides a new perspective for structural optimization in high-pressure tunnels. It not only enhances the ultimate internal pressure and improves the load-bearing ratio of the surrounding rock, but also reduces the required lining thickness and lowers construction costs, demonstrating substantial engineering applicability.

Under high internal pressure, crack development in the lining of compressed air energy storage (CAES) caverns is inevitable. To prevent the flexible sealing layer from being damaged by embedding into these cracks, its thickness design must account for crack embedment failure, a factor overlooked in current designs that primarily focus on air tightness. This study presents the first systematic experimental investigation into this failure mode. To address this, we designed and developed a novel test system capable of applying high-pressure gas (up to 15 MPa) across a simulated lining crack. Through a series of experiments with butyl rubber sealing layers of varying thicknesses and crack widths, we revealed the characteristic failure mechanism of flexible sealing materials under high pressure and established a thickness design curve for embedment resistance. The results show that the failure pressure decreases with an increasing crack width but increases significantly with layer thickness. For a controlled crack width of 1.0 mm, the maximum pressures withstood by thick layers of 1 mm and 2 mm were 6.42 MPa and 9.38 MPa, respectively. Based on the experimental results, a new design methodology incorporating crack embedment failure was proposed and applied to a planned CAES cavern project in Alxa, Inner Mongolia. The results demonstrate that for a cavern with a 10 m diameter and a controlled crack width of 1.0 mm, a thickness exceeding 2.8 mm is required to meet the air leakage rate requirement (<= 0.5% per day) from an air tightness perspective, while a minimum thickness of 3.0 mm is necessary to prevent embedment failure. Consequently, sealing layer design must consider both criteria simultaneously, as designs considering only air tightness may be unsafe. This study provides both a theoretical foundation and critical experimental data for the engineering design of flexible sealing layers in CAES caverns, offering significant practical value.

In China’s cold regions, insulation layers are commonly employed in numerous tunnels to mitigate frost-related damages. Nevertheless, despite these efforts, more than 70 ^∘ C, and the mean annual temperature falls below the initial temperature of the surrounding rock. Notably, when the temperature of the surrounding rock experiences a yearly decline, it results in freezing during the colder months, thereby exacerbating frost damage within the tunnels. This effect is attributed to the yearly accumulation of cold, which is a result of temperature cycles. Analyzing this effect and its impact on engineering is crucial for adopting effective frost-resistant measures. Research has been conducted using a temperature field numerical calculation model to study this effect under various conditions. The results show that conventional thickness insulation layers can prevent freezing in tunnels with a mean annual temperature greater than 2 ^∘ C in high-altitude regions and 3 ^∘ C in high-latitude regions. Low mean annual temperatures and their differences from initial ground temperatures are the primary causes of the cumulative freezing effect on cold-region tunnels. In the design of insulation layers for tunnels in cold regions, it is imperative to consider not only the mean temperature of the coldest month but also the mean annual temperature and its deviation from the initial ground temperature. When the cumulative freezing effect results in the failure of insulation layers in such tunnels, proactive measures to elevate both the mean annual temperature and ground temperature become crucial. By taking these factors into account, we can ensure a more effective and durable insulation design that can withstand the challenges posed by extreme cold conditions.

Energy geostructures represent a novel building energy-saving technology derived from ground source heat pump technology. Heat transfer and thermo-mechanical response characteristics stand out as pivotal issues in the investigation and design of such energy geostructures. This paper provides an overview of the research on heat transfer models, factors influencing heat exchange performance, and thermo-mechanical behaviour concerning energy piles, energy walls, and energy tunnels. The future perspectives were also presented. Four types consisting of ten basic heat transfer models for energy piles were summarized, and their advantages, limitations, and applicable scenarios were comprehensively discussed from multiple aspects. The heat transfer models for energy walls and energy tunnels are scarce, and only one model was introduced for each of them. The influences of some controllable design parameters on the thermal performance of energy geostructures and the thermal-induced mechanical behaviour were summarized. The key conclusions are that the fluid flow rate should not be too high or too low, which is generally considered sufficient to ensure that the flow state is turbulent; and properly intermittent operation is beneficial to the recovery of geothermy, thereby improving the heat exchange performance. Due to the differing conditions considered, it is not possible to draw a definitive conclusion regarding whether heating can increase or decrease the shaft resistance or bearing capacity of energy piles. Generally, thermal effects within energy walls are unlikely to cause severe damage to structural stability. The issues related to thermal-induced ground deformation are considered more critical than those concerning the energy tunnel structure deformation. This paper highlights the aspects that require further research and the new aspects worth exploring in the future. Energy geostructures are not limited to new construction projects, and combining with other renewable energy utilization methods and integrating into district energy networks are the future development trends.