IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p937-d1066095.html
   My bibliography  Save this article

Reliability Prediction of Tunnel Roof with a Nonlinear Failure Criterion

Author

Listed:
  • Xin Yang

    (Bangor College, Central South University of Forestry and Technology, Changsha 410004, China)

  • Jiangping Long

    (School of Civil Engineering, Central South University of Forestry and Technology, Changsha 410004, China)

Abstract

Based on the kinematics-based upper bound theorem and reliability theory, the stability of deep tunnel roofs in nonlinear Hoek-Brown media is investigated. The performance functions of rectangular and circular tunnels are proposed according to the roof collapse mode, respectively, with support pressure and pore water pressure being considered. With the proposed performance function of the rectangular tunnels, the first-order reliability method is utilized to perform reliability analysis. The rock strength parameters are regarded as random variables following the normal or lognormal distribution. To assess the validity of the obtained results, reliability indexes for different support pressure values are calculated and compared with solutions using the response surface method and Monte-Carlo simulation. The agreement shows that the first-order reliability method effectively evaluates the reliability index with the proposed performance function. Sensitivity analysis is performed to throw light on the significance of different random variables, and the impact of the variation coefficient on reliability indexes is discussed. For circular tunnels, MCS is utilized to evaluate the roof stability with the proposed performance function. The influences of the support pressure on the reliability index and the corresponding design points are investigated. The parametric study shows that the normal distribution of random variables has more influence on the failure probability than that of the lognormal distribution. However, the difference between the two distributions is small. σ t is the major factor that influences the reliability index compared to the B and r u . The supporting pressure for circular tunnels is smaller than that of rectangular tunnels when a target reliability index of 2.5 (failure probability equals 0.62%) is given.

Suggested Citation

  • Xin Yang & Jiangping Long, 2023. "Reliability Prediction of Tunnel Roof with a Nonlinear Failure Criterion," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:937-:d:1066095
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/937/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/4/937/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yu-Lin Lee & Ming-Long Zhu & Chi-Huang Ma & Chih-Sheng Chen & Chi-Min Lee, 2023. "Effect of Overburden Depth and Stress Anisotropy on a Ground Reaction Caused by Advancing Excavation of a Circular Tunnel," Mathematics, MDPI, vol. 11(1), pages 1-26, January.
    2. Baoping Chen & Bin Gong & Shanyong Wang & Chun’an Tang, 2022. "Research on Zonal Disintegration Characteristics and Failure Mechanisms of Deep Tunnel in Jointed Rock Mass with Strength Reduction Method," Mathematics, MDPI, vol. 10(6), pages 1-20, March.
    3. Jiadong Qiu & Fan Feng, 2022. "Effect of Different Tunnel Distribution on Dynamic Behavior and Damage Characteristics of Non-Adjacent Tunnel Triggered by Blasting Disturbance," Mathematics, MDPI, vol. 10(19), pages 1-19, October.
    4. Syed Mujtaba Hussaine & Linlong Mu, 2022. "Intelligent Prediction of Maximum Ground Settlement Induced by EPB Shield Tunneling Using Automated Machine Learning Techniques," Mathematics, MDPI, vol. 10(24), pages 1-25, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shaofeng Wang & Xin Cai & Jian Zhou & Zhengyang Song & Xiaofeng Li, 2022. "Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics," Mathematics, MDPI, vol. 10(18), pages 1-5, September.
    2. Yuanmin Wang & Yunqiang Wang & Song Luo & Hao Liu & Guansheng Yi & Kang Peng, 2023. "Influence of the Crack Angle on the Deformation and Failure Characteristics of Sandstone under Stepped Cyclic Uniaxial Compression with a Constant Lower Limit," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
    3. Linqi Huang & Shaofeng Wang & Xin Cai & Zhengyang Song, 2022. "Mathematical Problems in Rock Mechanics and Rock Engineering," Mathematics, MDPI, vol. 11(1), pages 1-3, December.
    4. Yongyi Wang & Bin Gong & Yongjun Zhang & Xiaoyu Yang & Chun’an Tang, 2022. "Progressive Fracture Behavior and Acoustic Emission Release of CJBs Affected by Joint Distance Ratio," Mathematics, MDPI, vol. 10(21), pages 1-30, November.
    5. Mohammad Javad Bozorgi & Masoud Parham & Omeid Rahmani & Ali Piroozian & Haylay Tsegab Gebretsadik & Syed Muhammad Ibad, 2022. "A Three-Dimensional Finite-Element Model in ABAQUS to Analyze Wellbore Instability and Determine Mud Weight Window," Energies, MDPI, vol. 15(9), pages 1-19, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:937-:d:1066095. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.