Analytic stress solutions for a circular pressure tunnel at pressure and great depth including support delay

Lu, Aizhong; Zhang, Luqing; Zhang, Ning

doi:10.1016/j.ijrmms.2010.09.002

Cited by 68 publications

(23 citation statements)

References 11 publications

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“…The last method is accurate but it cannot be solved in a closed-form solution. In most cases, the third case is chosen in the calculation of the deformation of the opening [9][10][11]. Here, we propose a novel closed-form solution with high accuracy based on the stress-strain relationship.…”

Section: Analytical Solutions For Stressesmentioning

confidence: 99%

“…For this reason, a large number of analyses of circular tunnel in an infinite medium subjected to a hydrostatic in situ stress have been presented by considering different models of material behavior, such as the ideal plastic, brittle plastic, strain-softening models, with the different yield criteria like the linear Mohr-Coulomb yield criterion and the nonlinear Hoek-Brown criteria. Detailed reviews of such works can be seen in [1][2][3][4][5][6][7][8][9][10][11]. Although there are numerical solutions for stresses and displacements such as FEM, but a closed-form solution is still preferred in a preliminary design.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Closed‐Form Solution for Circular Openings in Generalized Hoek‐Brown Media

Meng

Wang

2014

Mathematical Problems in Engineering

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A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

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Section: Analytical Solutions For Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Closed‐Form Solution for Circular Openings in Generalized Hoek‐Brown Media

Meng

Wang

2014

Mathematical Problems in Engineering

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“…Such projects have been increasingly emerging, such as the Mount Tenn� ozan Tunnel and Okura Tunnel in Japan and the Nazzano Tunnel in Italy, as well as the Damaoshan Tunnel of the Quanzhou Expressway, the Yuzhou Tunnel of the Chongqing Airport Road, and the expansion project of the Chongqing Eling Tunnel in China. During the tunnel construction, the mechanical response of the structure and the surrounding rock is an important parameter guiding the safe construction [1][2][3][4]. Researchers have extensively studied the effects of the single-tube tunnel excavation on the surface deformation and the mechanical response of the tunnel itself by using theoretical calculations [5,6], numerical simulation [7,8] and on-site monitoring [9,10].…”

Section: Introductionmentioning

confidence: 99%

Force and Deformation Characteristics during the Reconstruction and Expansion of Shallow Single-Tube Tunnels into Large-Span Multiarch Tunnels

Jia

Xia

Chen

et al. 2019

Advances in Materials Science and Engineering

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At present, there are an ever-increasing number of tunnel expansion projects in China. Studying the mechanical properties of the expanded tunnels is of great significance for guiding their safe construction. Through model testing and numerical simulation, the mechanical properties of a double-arch tunnel constructed through the expansion of the middle pilot heading from an existing single-tube tunnel were studied. The variation characteristics of the surface subsidence, surrounding rock stress, and stress and strain of the middle partition wall and lining during the tunnel reconstruction and expansion were investigated. The mechanism for transferring stress and strain between the left and right tunnel tubes was studied by a numerical simulation method. The results showed that the surface subsidence caused by the excavation of the left (i.e., the subsequent) tunnel tube was larger, and the maximum surface subsidence occurred at the right (i.e., the first) tunnel tube. The surrounding rock on the middle wall was the sensitive part of the tunnel excavation, the stress of the surrounding rock at the left spandrel of the right tunnel tube fluctuated and exhibited the most complex variation, and the stress of the surrounding rock at the right spandrel of the left tunnel tube exhibited the largest variation. The excavation of the left tunnel tube had a great influence on the forces of the middle partition wall and the lining structure of the right tunnel tube, the middle partition wall was subjected to eccentric compression towards the left tunnel tube, and the stress at the left spandrel under the initial support of the right tunnel tube exhibited complex variations. The excavation of the left and right tunnel tubes had a great influence on the stability of the surrounding rock, as well as on the force-induced deformation of the middle partition wall and the support structure, within the width of the single tunnel tube span behind the tunnel working face. Due to the different construction sequences, the stress and strain at the symmetric measurement points of the middle partition wall, as well as the left and right tunnel support structures, were very different.

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“…In addition, for lined circular tunnels [13][14][15], ITA report (2000) recommended the elastic equation method to determine the member forces and cross-section deformation of the segmental ring [16]. Lu et al (2011) applied the complex method and presented the stress solutions for a circular lined tunnel [17]. Yasuda et al (2017) established a two-dimensional elastic solution for a deep circular tunnel under the far-field static loading [18].…”

Section: Introductionmentioning

confidence: 99%

Analytic Solutions of the Forces and Displacements for Multicentre Circular Arc Tunnels

Han

Xia

2018

Mathematical Problems in Engineering

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A complex variable method for solving the forces and displacements for multicentre circular arc (MCA) tunnels by using analytical solutions is presented. The governing equations for the stresses and displacements are expressed in terms of series expression. Combined with the boundary conditions at lining inner region, lining-surrounding rock-mass interface, and infinity area, the undetermined coefficients of the analytic functions are obtained by solving a linear equation set. Forces solutions for linings are also presented according to the tangential stress at the two boundaries. Conformal mapping function for the MCA tunnel is given from the optimization method. Calculation results show that solutions with high accuracy can be obtained when the number of terms of power series is greater than 30. The effects of the degrees from the tunnel crown to the invert, coefficient of the lateral earth pressure, and distance from the rock-mass to the interface on regulations of the lining forces and rock-mass stresses are also thoroughly investigated.

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Analytic stress solutions for a circular pressure tunnel at pressure and great depth including support delay

Cited by 68 publications

References 11 publications

A Novel Closed‐Form Solution for Circular Openings in Generalized Hoek‐Brown Media

A Novel Closed‐Form Solution for Circular Openings in Generalized Hoek‐Brown Media

Force and Deformation Characteristics during the Reconstruction and Expansion of Shallow Single-Tube Tunnels into Large-Span Multiarch Tunnels

Analytic Solutions of the Forces and Displacements for Multicentre Circular Arc Tunnels

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