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A novel fractal-order elasto-visco-plastic creep damage model and its engineering-scale creep parameter determination method
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Qingzhe Cuia, Fei Wua, *, Jianfeng Liub, Jie Chena, Cunbao Lic, Renbo Gaoa, Shuo Gaoa, Yu Wanga, Huiqing Liua, Tao Rend
Underground Space | 2026, 27 : 216 - 235
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Underground Space | 2026, 27: 216-235
• Research Paper •
A novel fractal-order elasto-visco-plastic creep damage model and its engineering-scale creep parameter determination method
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Qingzhe Cuia, Fei Wua, *, Jianfeng Liub, Jie Chena, Cunbao Lic, Renbo Gaoa, Shuo Gaoa, Yu Wanga, Huiqing Liua, Tao Rend
Affiliations
  • aState Key Laboratory for the Coal Mine Disaster Dynamics and Controls, Chongqing University, Chongqing 400044, China
  • bState Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China
  • cState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
  • dChina Railway Changjiang Transport Design Group Co., Ltd., Chongqing 400020, China
Published: 2026-04-10 doi: 10.1016/j.undsp.2025.10.009
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The effective prediction and evaluation of the long-term stability of deep-buried tunnels are crucial for tunnel design, construction, and operation. The creep model is key to predicting time-dependent behavior, and the accuracy of time-dependent deformation predictions is determined by the creep parameters. This paper introduces a novel fractal-order elasto-visco-plastic creep damage (FEVPD) model that incorporates long-term strength into the damage evolution equation within the framework of continuum damage mechanics. The model effectively captures the three-stage creep behavior of various rock types and predicts their creep lifespans under different stress levels. The FEVPD model was implemented in FLAC3D using C++. Additionally, in determining the creep parameters of rock at the engineering scale to address the high computational cost of parameter inversion, an improved genetic algorithm was developed with adaptive perturbation, elitism, and dynamic mutation mechanisms. Application to field monitoring data from the Jinping II hydropower station tunnel demonstrated that the FEVPD model improved the prediction accuracy of time-dependent deformation by 32.68% compared to the classical Burgers-Mohr (CVISC) model. The enhanced inversion method also reduced the final error by 26.0% and 22.7% for the FEVPD and CVISC models, respectively, compared with the standard algorithm. Finally, this model was used to predict the long-term stability of the tunnel. The results provide a reliable and efficient framework for modeling and predicting creep behavior in deep rock engineering.

Fractal-order derivatives  /  Creep model  /  Numerical simulation  /  Parameter inversion  /  Improved genetic algorithm
Qingzhe Cui, Fei Wu, Jianfeng Liu, Jie Chen, Cunbao Li, Renbo Gao, Shuo Gao, Yu Wang, Huiqing Liu, Tao Ren. A novel fractal-order elasto-visco-plastic creep damage model and its engineering-scale creep parameter determination method[J]. Underground Space, 2026 , 27 : 216 -235 . DOI: 10.1016/j.undsp.2025.10.009
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Funding
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  • National Natural Science Foundation of China(52374078; U24A20616)
  • Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(2024TIAD-CYKJCXX0011)
  • Fundamental Research Funds for the Central Universities(2023CDJKYJH021)
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Year 2026 volume 27 Issue 0
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Article Info
doi: 10.1016/j.undsp.2025.10.009
  • Receive Date：2025-07-18
  • Online Date：2026-06-17
  • Published：2026-04-10
Article Data
Affiliations
History
  • Received：2025-07-18
  • Revised：2025-09-11
  • Accepted：2025-10-15
Funding
National Natural Science Foundation of China(52374078; U24A20616)
Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(2024TIAD-CYKJCXX0011)
Fundamental Research Funds for the Central Universities(2023CDJKYJH021)
Affiliations
    aState Key Laboratory for the Coal Mine Disaster Dynamics and Controls, Chongqing University, Chongqing 400044, China
    bState Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China
    cState Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
    dChina Railway Changjiang Transport Design Group Co., Ltd., Chongqing 400020, China

Corresponding:

* Corresponding author. E-mail address: (F. Wu).
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https://castjournals.cast.org.cn/joweb/undsp/EN/10.1016/j.undsp.2025.10.009
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Citations
表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
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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