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Modified linear superposition method for stress tensor field analysis and its application to compressed air energy storage chamber group
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Zeyuan Suna, Cheng Zhaoa, b, *, Qinyuan Luoa, Ran Huanga, Ning Jiac, Jinquan Xinga, b, Jialun Niua, b, Chao Weia
Underground Space | 2026, 27 : 112 - 131
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Underground Space | 2026, 27: 112-131
Research Paper
Modified linear superposition method for stress tensor field analysis and its application to compressed air energy storage chamber group
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Zeyuan Suna, Cheng Zhaoa, b, *, Qinyuan Luoa, Ran Huanga, Ning Jiac, Jinquan Xinga, b, Jialun Niua, b, Chao Weia
Affiliations
  • aDepartment of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
  • bKey Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
  • cNorth China Power Engineering Co., Ltd. of China Power Engineering Consulting Group, Beijing 100120, China
Published: 2026-04-10 doi: 10.1016/j.undsp.2025.03.010
Outline
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Burial depth and spacing are key factors influencing the stability of compressed air energy storage chamber groups. However, methods for determining safe burial depth and spacing in aligned multi-chamber systems remain underexplored. This study introduces a modified linear superposition method (M-LSM) for calculating elastic stress tensor fields in the surrounding rock around multiple chambers. The method analyzes the distribution of elastic stress under varying design parameters and surrounding rock conditions, identifying the most critical stress locations, which are the sidewalls affected by adjacent chambers, and providing deeper insights into stress concentrations caused by chamber interactions. The relationship between safe burial depth and spacing follows an approximately inverse proportionality, with the safety criterion of no plastic zones developing in the surrounding rock. A closed-form solution for safe burial depth and spacing is derived, which can be used to quickly determine the design parameters. The M-LSM is applicable to a wide range of internal pressurized chamber groups and borehole problems, capturing mutual interactions between adjacent chambers more realistically. Compared to finite element method simulations based on a practical engineering case, the results show errors that are typically negligible, validating the reliability of the analytical approach. This fully analytical method is mesh-free, iteration-free, and offers infinite resolution, making it highly efficient for both computations and practical applications. The closed-form solution derived from this method provides significant value for trend analysis, practical calculations, and engineering applications.

Linear superposition method  /  Compressed air energy storage  /  Burial depth  /  Chamber spacing  /  Chamber group  /  Closed-form solution
Zeyuan Sun, Cheng Zhao, Qinyuan Luo, Ran Huang, Ning Jia, Jinquan Xing, Jialun Niu, Chao Wei. Modified linear superposition method for stress tensor field analysis and its application to compressed air energy storage chamber group[J]. Underground Space, 2026 , 27 : 112 -131 . DOI: 10.1016/j.undsp.2025.03.010
  • Special Funds for Science and Technology Supports Carbon Peaking and Carbon Neutrality of the "Science and Technology Innovation Action plan" of Shanghai(22dz1205300)
  • Interdisciplinary Joint Research Project of Tongji University(2022-3-YB-05)
  • Major Science and Technology Projects of China Energy Engineering Corporation Limited 2021(CEEC2021-KJZX-04)
Year 2026 volume 27 Issue 0
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Article Info
doi: 10.1016/j.undsp.2025.03.010
  • Receive Date:2024-11-28
  • Online Date:2026-06-17
  • Published:2026-04-10
Article Data
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History
  • Received:2024-11-28
  • Revised:2025-02-09
  • Accepted:2025-03-21
Funding
Special Funds for Science and Technology Supports Carbon Peaking and Carbon Neutrality of the "Science and Technology Innovation Action plan" of Shanghai(22dz1205300)
Interdisciplinary Joint Research Project of Tongji University(2022-3-YB-05)
Major Science and Technology Projects of China Energy Engineering Corporation Limited 2021(CEEC2021-KJZX-04)
Affiliations
    aDepartment of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
    bKey Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China
    cNorth China Power Engineering Co., Ltd. of China Power Engineering Consulting Group, Beijing 100120, China

Corresponding:

* Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China. E-mail address: (C. Zhao).
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表12种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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