Analytical Solution for a Deep Circular Tunnel in Anisotropic Ground and Anisotropic Geostatic Stresses

Vitali, Osvaldo P.M.; Celestino, Tarcísio Barreto; Bobet, Antonio

doi:10.1007/s00603-020-02157-5

Cited by 25 publications

(6 citation statements)

References 39 publications

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“…Another property of interest in rock mechanics is anisotropy, which can be observed in many different types of rocks, such as metamorphic, sedimentary, rock salt or slate (Dubey and Gairola 2008;Mánica 2018;Vitali et al 2020;Alejano et al 2021). Regarding the cross-anisotropy, two main directions of anisotropy (parallel and orthogonal to the bedding plane) are generally identified.…”

Section: Anisotropic Behaviour Of Geomaterialsmentioning

confidence: 99%

“…It would introduce significant errors in the mechanical analyses if the anisotropy of geomaterials is incorrectly considered as isotropy (Barla 1972;Kanfar et al 2015). Based on the cross-anisotropic constitutive model, some researchers have developed solutions to analyse the effect of anisotropy on tunnelling works, such as deeply circular tunnels (Hefny and Lo 1999;Vitali et al 2020), shallow circular (2022) 8:146 tunnels (Zymnis et al 2013), triangular holes (Daoust and Hoa 1991), arbitrary cross-section tunnels (Tran Manh et al 2015a;Lu et al 2017), or twin circular tunnels (Tran-Manh et al 2015). Considering threedimensional (3D) problems, some researchers (Tonon and Amadei 2002;Franzius et al 2005) investigated the effect of anisotropy on the ground settlement.…”

Section: Introductionmentioning

confidence: 99%

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Modelling underground excavations in rock masses with anisotropic time-dependent behaviour

Song

Rodríguez-Dono

Farfan

2022

Geomech. Geophys. Geo-energ. Geo-resour.

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When modelling rock masses that behave anisotropically and in addition present a time dependent behaviour, it is relevant to select a constitutive model able to represent their actual behaviour realistically. This article presents an alternative anisotropic time-dependent constitutive model able to predict the coupling between anisotropic behaviour and time-dependent (or viscous) behaviour. The viscous behaviour is simulated with the Burgers model and all elastic springs and viscous dashpots are considered to exhibit transversely isotropic properties. The proposed constitutive model has been implemented in the finite element method software CODE_BRIGHT. To verify the basic anisotropic elastic solution, it has been compared with that of PLAXIS results. And to verify the isotropic viscoelastic solution, it has been compared with analytical solutions. Furthermore, the proposed constitutive model has been used to predict the behaviour of samples from laboratory tests. Finally, parametric analyses have been carried out to investigate the influence of different factors on tunnelling responses, including the selection of different constitutive models, anisotropy of initial stresses and anisotropy of material properties. The proposed model provides an alternative method for the preliminary design of geotechnical engineering works involving geomaterials that exhibit anisotropic time-dependent behaviour.Article highlights • An anisotropic time-dependent model has been implemented in CODE_BRIGHT and validated. • The model can predict the coupled anisotropic time-dependent behaviour of geomaterials. • Parametric analyses have been performed to study the influence of different factors in ground response.

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Section: Anisotropic Behaviour Of Geomaterialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling underground excavations in rock masses with anisotropic time-dependent behaviour

Song

Rodríguez-Dono

Farfan

2022

Geomech. Geophys. Geo-energ. Geo-resour.

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“…Far-behind the face, the deformed cross section in both cases is exactly the same, which shows that the far-field axial shear stress does not affect the radial displacements far-behind the face. This is because, when the tunnel axis is aligned with one of the principal material directions, in-plane and out-of-plane deformations are decoupled (Vitali et al, 2020).…”

Section: Tunnel In Horizontally Structured Rock Massmentioning

confidence: 99%

Tunnel Misalignment with Geostatic Principal Stress Directions in Anisotropic Rock Masses

Vitali¹,

Celestino²,

Bobet³

2020

S&R

Self Cite

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Rock masses may present pronounced stress anisotropy, and so it is likely that a tunnel is misaligned with the geostatic principal stress directions. As a consequence, anti-symmetric axial displacements and axial shear stresses are induced around the tunnel due to the presence of far-field axial shear stresses. Limited research has been conducted on the effects of far-field axial shear stresses on tunnel behavior. This paper investigates the effects of tunnel misalignment with the geostatic principal stresses in anisotropic rock masses. 3D FEM modeling of a tunnel misaligned 45°with the principal horizontal stresses is conducted. An anisotropic geostatic stress field is considered, with the major horizontal stress two times larger than the vertical stress and the minor horizontal stress equal to the vertical stress. The anisotropic behavior of the rock mass is represented by a transversely anisotropic elastic model, with properties typical of anisotropic rock masses. Tunnels in horizontally and vertically-structured rock masses are assessed. Unsupported and supported tunnels are investigated. The results show that asymmetric deformations and asymmetric stresses are induced near the face of the tunnel as a result of the tunnel misalignment with the geostatic principal stresses and with the rock mass structure. These asymmetric deformations near the face affect the ground-support interaction such that the internal forces in the liner are also asymmetric.

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“…Through a comprehensive review of existing analytical solutions, theoretical solutions for deep (Muskhelishvili, 1953) and shallow tunnels (Exadaktylos et al, 2002;Lu et al, 2021;Verruijt, 1997Verruijt, , 1998Wang et al, 2018) were developed. Various constitutive models have been employed to characterize the mechanical properties of surrounding rocks, such as elasticity, plasticity (Xu et al, 2015;Zareifard et al, 2021), time-dependency (Wang et al, 2019;Wang et al, 2017) or anisotropy (Hefny et al, 1999;Vitali et al, 2020) However, the aforementioned studies were conducted without considering hydro-mechanical coupling behaviors, yet when involving engineering applications in water-rich regions, the majority of deep tunnels are excavated beneath the groundwater table (Lee et al, 2004;Song et al, 2021a;Song et al, 2021b).…”

Section: Introductionmentioning

confidence: 99%

Hydro-mechanical theoretical solutions of supported noncircular excavated in deep elastic ground

Wang,

Song

et al. 2024

Preprint

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This study provides a general analytical approach to predict the stresses and displacements of deep noncircular tunnels excavated in saturated elastic ground, considering the hydro-mechanical coupling, the interaction between rock and liner, and arbitrary tunnel shapes. The complex variable theory is innovatively extended to solve the seepage fields for noncircular supported tunnels in both surrounding rocks and liner fields. After that, coupled hydro-mechanical solutions of stresses and displacements can be determined by considering the influence of seepage flow on the mechanical responses. Furthermore, stability analyses of supported tunnels are conducted in the hydro-mechanical coupled framework, incorporating the effect of seepage flow. As a verification, a good agreement is observed between stress and displacement fields obtained from the current analytical solutions and numerical simulations. Then, parametric analyses are performed to assess how variations in tunnel shape, liner permeability, and liner thickness influence the mechanical behaviours of supported tunnels. Meanwhile, by employing the Mohr-Coulomb strength criterion, an expression of equivalent stress is proposed to assess the potential failure behaviour of supported tunnels in the entire process of excavation and operation stages. This study provides high potential of application to a number of relevant case studies, such as tunnelling below the water table.

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Analytical Solution for a Deep Circular Tunnel in Anisotropic Ground and Anisotropic Geostatic Stresses

Cited by 25 publications

References 39 publications

Modelling underground excavations in rock masses with anisotropic time-dependent behaviour

Modelling underground excavations in rock masses with anisotropic time-dependent behaviour

Tunnel Misalignment with Geostatic Principal Stress Directions in Anisotropic Rock Masses

Hydro-mechanical theoretical solutions of supported noncircular excavated in deep elastic ground

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