Fractional Modeling of Deep Coal Rock Creep Considering Strong Time-Dependent Behavior

Shuai Yang, Wenhao Jia (), Senlin Xie (), Haochen Wang and Lu An
Additional contact information
Shuai Yang: College of Energy and Mining Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
Wenhao Jia: Information Institute of the Ministry of Emergency Management of the PRC, Beijing 100029, China
Senlin Xie: College of Energy and Mining Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
Haochen Wang: Information Institute of the Ministry of Emergency Management of the PRC, Beijing 100029, China
Lu An: State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

Mathematics, 2025, vol. 13, issue 20, 1-19

Abstract: Deep coal rocks exhibit strong time-dependent behavior, including significant plastic deformation and large tunnel displacements, which complicate tunnel support in deep underground engineering. A fractional creep model considering strong time-dependence was developed based on the classical Nishihara framework to capture this behavior. Additional time-dependent strains induced by stress-state variations were considered, with long-term rock strength adopted as the damage stress threshold. The stress difference between nominal and post-damage stress, σ D ( t ) , defined as the stress gradient, was applied to a viscoelastic–plastic body containing a fractional Abel dashpot, producing conventional creep strain and strong time-dependent strain. The model was extended from one-dimensional to three-dimensional under triaxial stress conditions. The validity of the model was verified using triaxial creep test data for argillaceous sandstone and coal in deep roadways, and the model parameters were determined. The results demonstrate that the model accurately reproduces the full creep process, particularly the nonlinear accelerated stage influenced by strong time-dependence. Through stress-gradient-induced variations in strong time-dependent strain, the proposed creep model elucidates the progression of deformation in the strong time-dependent stage, offering a theoretical framework for the quantitative assessment of deep rock’s strong time-dependence. Sensitivity analysis identified the stress level, fractional order, and strong time-dependence coefficient α as key factors affecting strong time-dependent creep behavior. These findings indicate that tunnel support structures in deep environments are prone to instability, underscoring the necessity of accounting for strong time-dependence to ensure long-term stability.

Keywords: strong time-dependent behavior; fractional derivative; creep model; stress gradient; deep coal rock (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/20/3247/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/20/3247/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:20:p:3247-:d:1768122

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().