2D and 3D upper bound solutions for tunnel excavation using ‘elastic’ flow fields

Klar, Assaf; Osman, Ashraf S.; Bolton, M. D.

doi:10.1002/nag.597

Cited by 95 publications

(38 citation statements)

References 7 publications

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“…Some writers have considered a purely cohesive soil ͑Broms and Bennermark 1967 ;Mair 1979;Davis et al 1980;Kimura and Mair 1981;Ellstein 1986;Augarde et al 2003;Klar et al 2007; among others͒. In this case, the stability of a tunnel face is governed by the so-called load factor N defined as N = ͑ s + ␥H − t ͒ / c u where s ϭsurcharge loading on the ground surface; t ϭuniform pressure applied on the tunnel face; Hϭdepth of the tunnel axis; and c u ϭsoil undrained cohesion.…”

Section: Introductionmentioning

confidence: 99%

“…This promising approach is currently limited to a two-dimensional analysis. Finally, Klar et al ͑2007͒ have suggested a new kinematical approach in limit analysis theory for the 2D and 3D stability analysis of circular tunnels in a purely cohesive soil. Their method is based on an admissible continuous velocity field.…”

Section: Introductionmentioning

confidence: 99%

“…The soil considered in the analysis is assumed to be frictional and/or cohesive. The main originality of the present work is that the failure mechanism presented herein includes the whole circular tunnel face while the existing mechanisms ͓except that developed by Klar et al ͑2007͒ in the case of a purely cohesive soil͔ only involve an elliptical area inscribed to the circular face. This improvement required numerical generation "point by point" of complex shapes of failure surfaces instead of simple use of existing standard geometric shapes ͑such as cones or cylinders͒ as it was made in Davis et al ͑1980͒, Leca and Dormieux ͑1990͒, and Mollon et al ͑2009͒.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

Mollon

Dias

Soubra

2010

J. Geotech. Geoenviron. Eng.

296

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Abstract:The aim of this paper is to determine the face collapse pressure of a circular tunnel driven by a pressurized shield. The analysis is performed in the framework of the kinematical approach of limit analysis theory. It is based on a translational three-dimensional multiblock failure mechanism. The present failure mechanism has a significant advantage with respect to the existing limit analysis mechanisms developed in the case of a frictional soil: it takes into account the entire circular tunnel face and not only an inscribed ellipse to this circular area. This was made possible by the use of a spatial discretization technique. Hence, the three-dimensional failure surface was generated "point by point" instead of simple use of existing standard geometric shapes such as cones or cylinders. The numerical results have shown that a multiblock mechanism composed of three blocks is a good compromise between computation time and results accuracy. The present method significantly improves the best available solutions of the collapse pressure given by other kinematical approaches. Design charts are given in the case of a frictional and cohesive soil for practical use in geotechnical engineering.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

Mollon

Dias

Soubra

2010

J. Geotech. Geoenviron. Eng.

296

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“…It requires the determination of a so-called "critical collapse pressure" of the tunnel face (denoted σ c ); that is, the smallest applied pressure necessary to prevent soil collapse. This issue has been extensively studied by several writers in the case of purely cohesive soils (Broms and Bennermark 1967;Davis et al 1980;Ellstein 1986;Augarde et al 2003;Klar et al 2007; among others) and in the case of frictional soils with or without cohesion (Leca and Dormieux 1990;Chambon and Corté 1994;Eisenstein and Ezzeldine 1994;Anagnostou and Kovari 1996;Mollon et al 2009aMollon et al , b, 2010among others). All studies cited except those by Mollon et al (2009a, b) were deterministic.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of Pressurized Tunnels against Face Stability Using Collocation-Based Stochastic Response Surface Method

Mollon

Dias

Soubra

2011

J. Geotech. Geoenviron. Eng.

110

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A probabilistic analysis of the face stability of a tunnel driven by a compressed-air pressurized shield is presented. The collocation-based stochastic response surface methodology (CSRSM) is used. The deterministic model employed in the probabilistic analysis is analytical. A translational multiblock collapse mechanism in the framework of the kinematic theorem of limit analysis forms the basis of the analysis. The soil friction angle and cohesion are considered as random variables. CSRSM was first validated by the comparison of the results obtained from the original analytical deterministic model. Then, the influence of the probabilistic characteristics of the uncertain variables was studied. Contrary to the correlation between c and φ and the coefficients of variation of these variables, which have a significant effect on the variability of the critical collapse pressure, the nonnormality of the distributions of the random variables was shown not to have a considerable effect on the distribution of the output.

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“…They assumed that the soil deforms compatibly following a Gaussian distribution within the boundaries of this deformation mechanism and is rigid outside this mechanism. Klar et al [13] suggested a new kinematical approach in limit analysis theory for the 2D and 3D stability analysis of circular tunnels in a purely cohesive soil. The velocity fields in the 2D and 3D stability analyses are based on the analytical works of Verruijt and Booker [14] and Sagaseta [15], respectively.…”

Section: Introductionmentioning

confidence: 99%

Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

Zhang

Han

2015

Mathematical Problems in Engineering

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This paper investigates the collapse mechanisms and possible collapsing block shapes of shallow unlined tunnels under conditions of plane strain. The analysis is performed following the framework from a branch of catastrophe theory, functional catastrophe theory. First, the basic principles of functional catastrophe theory are introduced. Then, an analytical solution for the shape curve of the collapsing block of a shallow unlined tunnel is derived using functional catastrophe theory based on the nonlinear HoekBrown failure criterion. The effects of the rock mass parameters of the proposed method on the shape and weight of the collapsing block are examined. Moreover, a critical cover depth expression to classify deep and shallow tunnels is proposed. The analytical results are consistent with those obtained by numerical simulation using the particle flow code, demonstrating the validity of the proposed analytical method. The obtained formulas can be used to predict the height and width of the collapsing block of a shallow unlined tunnel and to provide a direct estimate of the overburden on the tunnel lining. The obtained formulas can be easily used by tunnel engineers and researchers due to their simplicity.

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2D and 3D upper bound solutions for tunnel excavation using ‘elastic’ flow fields

Cited by 95 publications

References 7 publications

Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

Probabilistic Analysis of Pressurized Tunnels against Face Stability Using Collocation-Based Stochastic Response Surface Method

Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

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