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An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method

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Title: An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method
Authors: Yu-Lin Lee, Chi-Huang Ma, Chi-Min Lee
Source: Mathematics, Vol 11, Iss 15, p 3389 (2023)
Publisher Information: MDPI AG, 2023.
Publication Year: 2023
Collection: LCC:Mathematics
Subject Terms: convergence–confinement method, non-linear failure criterion, closed-form solution, incremental procedure, Mathematics, QA1-939
More Details: The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends.
Document Type: article
File Description: electronic resource
Language: English
ISSN: 2227-7390
Relation: https://www.mdpi.com/2227-7390/11/15/3389; https://doaj.org/toc/2227-7390
DOI: 10.3390/math11153389
Access URL: https://doaj.org/article/51701419fb1640de99976d7dc672543a
Accession Number: edsdoj.51701419fb1640de99976d7dc672543a
Database: Directory of Open Access Journals
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  Data: An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method
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  Data: <searchLink fieldCode="AR" term="%22Yu-Lin+Lee%22">Yu-Lin Lee</searchLink><br /><searchLink fieldCode="AR" term="%22Chi-Huang+Ma%22">Chi-Huang Ma</searchLink><br /><searchLink fieldCode="AR" term="%22Chi-Min+Lee%22">Chi-Min Lee</searchLink>
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  Data: Mathematics, Vol 11, Iss 15, p 3389 (2023)
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  Data: MDPI AG, 2023.
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  Data: The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends.
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        StartPage: 3389
    Subjects:
      – SubjectFull: convergence–confinement method
        Type: general
      – SubjectFull: non-linear failure criterion
        Type: general
      – SubjectFull: closed-form solution
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      – SubjectFull: incremental procedure
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      – TitleFull: An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method
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            NameFull: Chi-Min Lee
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