A unified constitutive model for yielding single-lining tunnel supports with resistance limiters under large deformation.

Muhammad Zohaib, Qiu Wenge, Muhammad Awais Hussain, Weipeng Pan, Muhammad Akbar, Tarek Salem Abdennaji, Aymen Flah

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Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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5 · Who and what money

Authors and funding

7 authors.

Muhammad ZohaibKey Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, People's Republic of China. zohaib06@my.swjtu.edu.cn.

Qiu WengeKey Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, People's Republic of China.

Muhammad Awais HussainCollege of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, Zhejiang, China. awaishussain@zju.edu.cn.

Weipeng PanKey Laboratory of Transportation Tunnel Engineering, Ministry of Education, School of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031, People's Republic of China.

Muhammad AkbarDepartment of Civil Engineering, College of Engineering, Northern Border University, 73222, Arar, Saudi Arabia. akbarmohammad0092@gmail.com.

Tarek Salem AbdennajiDepartment of Civil Engineering, College of Engineering, Northern Border University, 73222, Arar, Saudi Arabia.

Aymen FlahApplied Science Research Center, Applied Science Private University, Amman, 11931, Jordan.

Funding

Increasing the resilience of power grids in the context of decarbonisation, decentralisation and sustainable socioeconomic development CZ.02.01.01/00/23_021/0008759Northern Border University, Arar, KSA, NBU-FFMRA-2026-3561-03Southwest Jiaotong University 51991395

6 · The paper itself

Abstract

Large deformation in soft rock tunnels remains a critical challenge in mining and underground engineering, with conventional rigid supports prone to overstressing and failure due to limited deformation compatibility. Although yielding supports with resistance limiters such as inflatable airbags and circular steel bellows (CSBs) provide improved adaptability, current design approaches remain largely empirical or overly simplified. As a result, they lack a unified constitutive framework that can quantitatively describe their multi-stage mechanical behavior and effectively link it to performance-based design. To address this gap, this study develops and experimentally validates a novel constitutive model that characterizes yielding supports through three explicit phases: elastic yielding (initial stiffness k

Indexed as

Constitutive modelEnergy-reaction coupling coefficientMining and underground engineering, Support adaptability indexSqueezing groundStrain uniformity indexYielding tunnel support

Identifiers

PMID42336883

DOI10.1038/s41598-026-53808-6

PMCPMC13550495

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.