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Geomechanics and Engineering
  Volume 22, Number 1, July10 2020 , pages 11-23

A new analytical-numerical solution to analyze a circular tunnel using 3D Hoek-Brown failure criterion
Masoud Ranjbarnia, Nima Rahimpour and Pierpaolo Oreste

    In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.
Key Words
    circular tunnel; stress and strain; stiffness matrix; analytical solution; three dimensional Hoek-Brown criterion; stress invariants
Masoud Ranjbarnia and Nima Rahimpour: Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Tabriz, 29 Bahman Blvd, Tabriz, Iran

Pierpaolo Oreste: Department of Environmental, land and infrastructure Engineering, Politecnico di Torino, Corso Duca degli Abruzzi, Torino 24-10129, Italy

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