Masonry tunnels are underground structures which can experience degradation due to ageing resulting in damage or cracking. In this work, the stability of these structures is studied using the upper-bound kinematic approach of yield design theory. This method allows estimating the ultimate load of any system knowing the geometry and the strength of its constitutive materials. However, the determination of the optimal failure mechanism, that is to say the one giving the upper-bound of the ultimate load, can be tricky as regards the interactions between the ground and the structure itself. To overcome this issue, it has been chosen to decompose the problem in two sub-problems. On the one hand, existing kinematic models dealing with the stability of excavations are extended to cohesive-frictional grounds. On the other hand, a mechanism representing the deformation observed on-field is explored to assess the masonry lining stability. Yield design theory is used to determine upper-bound estimations of the ultimate load for excavations in purely frictional grounds, cohesive-frictional grounds, and for a masonry vault subjected to a concentrated load.

Field monitoring programs (e.g., convergence measurements and stress measurements in the support system) play an important role in following the response of the ground and of the support system during and after excavation. They contribute to the adaptation of the excavation and support installation method and the prediction of the long-term behavior. In the context of the Lyon-Turin link project, an access gallery (SMP2) was excavated between 2003 and 2010, and a survey gallery (SMP4) has been excavated since 2017. Both tunnels are excavated in Saint-Martin-la-Porte (France) across a strongly tectonized Carboniferous formation, which is highly fractured and heterogeneous. Squeezing behavior has been observed and led to the instability of the support system and of the tunnel face in various locations. Based on the knowledge gained from field data processing and numerical modeling in SMP2, new field data are analyzed for SMP4, which is excavated at a much deeper depth, with a different orientation and with different excavation methods. Numerical modeling of the various profiles of SMP4 considering the excavation stages and the specific yielding support is presented, which predicts the time-dependent response of the tunnel.

A squeezing Carboniferous formation was met at a depth of 300 m during the excavation of the Saint-Martin-la-Porte access gallery (SMP2) in France within the Lyon-Turin railway link project. Large, time-dependent and anisotropic deformation was observed around the tunnel wall during and after excavation, and difficulties related to tunneling in squeezing ground have been encountered. An anisotropic visco-elastic plastic constitutive law (Tran- Manh et al. 2015) has been proposed in order to model the ground behavior. This model was validated by field auscultation carried out in SMP2. As a part of the base tunnel, a new survey gallery (SMP4) began to be excavated in the recent years across the same squeezing rock formation at a depth of about 600 m. A yield control support system was adopted in the zones of large deformation, which contains highly deformable concrete elements to stabilize the high convergence (Bonini and Barla 2012). In the present work, the studies of SMP2 are extended to SMP4 by considering the constitutive model developed for SMP2. The innovative excavation and support method is taken into account. Numerical modeling is performed using FLAC3D to analyze the tunnel response. A good agreement can be obtained between the field measurements and the numerical results.

L’estimation des déplacements induits par le creusement au tunnelier sur des constructions avoisinantes (immeubles, ouvrages d’art, tunnels, réseaux…) est une étape essentielle des projets d’ouvrages souterrains en zones urbaines. De cette estimation sont, en effet, déduits ou adaptés des choix forts de conception tels que le tracé du tunnel, le dimensionnement du tunnelier (surcoupe, conicité…) et le choix de ses paramètres de pilotage (pression frontale, pression de bourrage…). Cet article présente des comparaisons entre les résultats de calculs éléments finis 2D et six sections instrumentées d’ouvrages réels. L’ensemble des paramètres nécessaires à la modélisation (modèle géotechnique et paramètres de creusement du tunnelier) est décrit de manière explicite. Ces rétro-analyses permettent de mieux cerner les paramètres clés du problème, en particulier le rôle majeur des pertes de volume induites le long de la jupe du tunnelier.

Tunnel excavation in squeezing ground exhibits large time-dependent and often anisotropic deformation. Within the context of the Fréjus road tunnel and its safety gallery excavated under the Alps between France and Italy, an interesting configuration of two parallel tunnels under squeezing ground conditions is observed. The special feature of this case study lies in the fact that both tunnels have been excavated in similar geotechnical conditions but with different excavation techniques. The road tunnel was excavated with conventional drill and blast methods in the 70s, whereas the safety gallery was excavated between 2009 and 2016 with a single-shield tunnel boring machine (TBM). This paper presents monitoring data processing and numerical simulations of both tunnels with the aim of studying the influence of the excavation method on the time-dependent tunnel response. A calibration of a visco-elasto-plastic anisotropic constitutive model based on the back-analysis of convergence measurements retrieved during the excavation of the Fréjus road tunnel is carried out. The identified ground behavior can be extrapolated to the parallel zones of the safety gallery. In particular, we are interested in the prediction of the stress state in the segmental lining of the gallery during its excavation and the comparison with in situ measurements. It is shown that the time-dependent behavior of the ground is affected by the excavation technique. Finally, an attempt to predict the long-term response of both tunnels is proposed.

The ConVergence-ConFinement (CV-CF) method is widely used in conventional tunneling at a preliminary stage of the design. In this method, the rock–support interaction is simplified by means of a two-dimensional plane-strain assumption. However, when the ground exhibits large deformation and/or when the support is very stiff and installed close to the tunnel face, the results obtained with the CV-CF method may significantly differ from those obtained using 3D numerical computations. The strong interaction taking place between the rigid lining and the rock mass is not considered in the most common use of the CV-CF method. Some improvements of the CV-CF method as the so-called implicit methods have been developed to better account for this interaction. In this paper, the applicability of the CV-CF methods is discussed for full-face excavation tunneling with a stiff support system. An in-depth comparison between plane-strain closed form solutions and numerical results which properly accounts for the 3D effects at the vicinity of the tunnel face is carried out. The range of application of the different approaches of the CV-CF method is discussed. Finally, some simple empirical formulae which can be used in preliminary design for a large range of ground conditions are proposed.

Frejus tunnel and its safety gallery between France and Italy in the Alps exhibit an interesting configuration of two parallel tunnels excavated in squeezing ground. They have a similar size and have been executed with different techniques. The road tunnel was excavated with traditional methods in the seventies and its safety gallery was excavated between 2009 and 2016 with a single-shielded TBM. The analysis of monitoring data collected from the road tunnel over a period of a few months before the installation of the final lining provides an accurate evaluation of the time-dependent response of the rock mass. The present work presents a comprehensive study of the convergence measurements retrieved from Frejus road tunnel and from its safety gallery and proposes the identification of zones with a similar response for both tunnels. The focus of the paper is on the calibration of a visco-plastic anisotropic constitutive model based on the convergence measurements of Frejus road tunnel. The information obtained from the study of the road tunnel can be extrapolated to the zones of the gallery showing a similar behavior. This allows carrying out a back-analysis of the safety gallery response using the proposed model.

This paper brings new elements of understanding on the stress-strain behaviour of soils during tunnel excavation using earth pressure balance shields (EPBS), thanks to laboratory tests carried out with an original reduced-scale physical model. Typical experiment results obtained during tunnelling with different soil types (purely frictional, cohesive-frictional) and different geometries (homogeneous or stratified grounds) are presented and discussed. These results mainly concern the soil stress-strain behaviour around the tunnel boring machine (TBM) and the soil-machine interaction at ideal rates of excavation. Firstly, results concerning the identification of pertinent control parameters to guarantee the safe advancement of the machine and the ground-supporting function of the cutting wheel are analysed. Surface settlements, stresses and displacements around the tunnel and behind the tunnel face, as well as arching effects around the shield are then presented and discussed.

Time-dependent response of deep tunnels is studied considering the progressive degradation of the mechanical properties of the rock mass. The constitutive model is based on a rock-aging law for the uniaxial strength of the rock and for the Young’s modulus. A semi-analytical solution is developed for the stresses and displacements around a deep circular tunnel taking into account the face advance. The evolution of the plastic and damage zones over time is determined. Numerical examples are presented for the case of Saint-Martin-La-Porte access adit in France of the Lyon–Turin Base Tunnel. The computed results which are compared with the field data in terms of the convergence of tunnel wall and of the displacements inside the rock mass monitored by multi-point extensometers show the efficiency of the approach to simulate the time-dependent deformation of a tunnel excavated in squeezing ground. Simple relationships are proposed to evaluate the parameters of the constitutive model directly from those of the empirical convergence law presented in previous work.

Closed-form solutions are of great interest for quick and accurate evaluation of stresses and displacements around underground excavations. Based on complex variable theory and on the method of conformal mapping, closed-form solutions for stresses and displacements around deep tunnels with arbitrary cross section in a homogeneous, transversely isotropic and linear elastic ground with non-isotropic far-field stress conditions are developed. The results obtained with the proposed analytical solution are compared with those obtained with the numerical code FLAC3D for some usual shapes of tunnel openings.

The problem of a single tunnel in anisotropic ground has been largely studied in the literature but the interaction of two tunnels is mostly addressed for the isotropic case. Simple superposition of the solutions of two non-interacting tunnels may give reasonable results if the distance between the tunnels is large enough, but fails when the tunnels are excavated close to each other. Based on complex variable theory, closed-form solutions for the stresses and displacements around two deep circular tunnels in a homogeneous, transversely isotropic and linear elastic ground with non-isotropic far-field stress conditions are developed. The results obtained with the proposed analytical solution are compared with those obtained with the numerical code Flac3D. The effects of the orientation of the isotropic plane and of the distance between two tunnels on the stress and displacements fields are discussed.

Most of the viscoplastic models used to describe the constitutive behavior of squeezing grounds assume isotropic deformation. However, it is commonly observed that squeezing behavior is characterized not only by large time-dependent but also often by anisotropic deformations. This study uses a semi-empirical approach based on the analysis of convergence measurements and a numerical model that takes into account the time-dependent and the anisotropic response of the rock mass to investigate the squeezing behavior of the Saint-Martin-la-Porte access gallery, excavated within the Lyon–Turin railway project. We first show how the semi-empirical convergence law of Sulem et al. (Int J Rock Mech Min Sci Geomech Abstr 24(3):155–164, 1987a ; Int J Rock Mech Min Sci Geomech Abstr 24(3):145–154, 1987b ) can be extended to anisotropic tunnel closure by considering an elliptical deformation of the rock mass and by fitting the convergence data along the principal axes of deformation. A new anisotropic time-dependent constitutive model is then proposed. This model includes ubiquitous joints of specific orientation embedded in an isotropic viscoplastic medium. This model is implemented in FLAC3D and numerical simulations are performed to back-analyze the anisotropic closure of the Saint-Martin-la-Porte access gallery. An efficient two-step procedure for calibrating the model parameters is proposed: the parameters of the isotropic solid matrix are first estimated by performing axisymmetric numerical simulations. The parameters of the ubiquitous joints are then calibrated by performing 3D computations. It is shown that the numerical results reproduce very well the convergence measurements of the studied sections of Saint-Martin-la-Porte gallery.

In this paper, we analyse the convergence measurements recorded in a gallery excavated in severely squeezing ground. The procedure consists in a preliminary geometrical treatment of the raw data to evaluate the principal axes of deformation by assuming an elliptic deformation of the walls of the gallery. Then the convergence law proposed by Sulem et al. (Int J Rock Mech Min Sci Geomech Abstr 24(3):145–154, 1987a), which is extended to account for anisotropic closure, is fitted on the displacements along the two axes of the obtained ellipse. This procedure is more robust and relevant than fitting the convergence recorded on the most deforming segment or fitting the average value of the convergence along the various segments. An attempt is made to correlate the amount and the direction of anisotropic deformation with the lithology and some geological features described by the dominant discontinuity families.

The capacity of a commercially available miniature pressure sensor for measuring stress evolutions in a partially saturated soil under quasi-static loads is studied, in view of its later application in laboratory-scale physical models. An extensive calibration program is first performed on a triaxial cell under isotropic loadings. These calibration tests provide useful data for assessing the uncertainty in stress measurements, especially in the case of partially saturated granular materials. Notably, influences of soil density, water content, and average grain size on stress measurements are quantified. Following these tests, an example of stress measurements on an original reduced-scale model of "earth pressure balance shield" (EPBS) is presented, which involves three-dimensional arching effects developing around the shield during excavation.

A semi-analytical solution based on the transfer matrix technique is proposed to analyze the stresses and displacements in a two-dimensional circular opening excavated in transversely isotropic formation with non-linear behavior. A non-isotropic far field can be accounted for and the process of excavation is simulated by progressive reduction of the internal radial stress. A hyperbolic stress–strain law is proposed to take into account the non-linear behavior of the rock. The model contains seven independent parameters corresponding to the five elastic constants of an elastic material with transverse isotropy and to the friction coefficient and cohesion along the parallel joints (weakness planes). This approach is based on the discretization of the space into concentric rings. It requires the establishment of elementary solutions corresponding to the stress and displacement fields inside each ring for given conditions at its boundaries. These solutions, based on complex variable theory, are obtained in the form of infinite series. The appropriate number of terms to be kept for acceptable approximation is discussed. This non-linear model is applied to back analyze the convergence measurements of Saint-Martin-la-Porte access gallery. Short-term and long-term ground parameters are evaluated.

Mechanisms of face collapse and face blow-out of tunnels driven in soft grounds with pressurized shield tunnel boring machine are studied. Results presented are issued from several tests carried out with an original laboratory reduced-scale model of earth pressure balanced shield (EPBS). The failure kinematics and limit face pressures in homogeneous purely frictional or cohesive-frictional soils, as well as in stratified soils (two or three-layered soils) are presented and analyzed. Comparisons of these experimental results with the predictions from yield design theory are discussed. (c) 2012 Elsevier Ltd. All rights reserved.

ABSTRACT Within the framework of the kinematic approach of yield design theory, a new 3D failure mechanism, in the shape of a rhinoceros horn and based on logarithmic-spirals, is presented for the stability analysis of the tunnel face in cohesive-frictional material. The model leads to a kinematic bound, on the unsafe side, of the critical face pressure which appears better (thus safer) than existing solutions. The case of shallow tunnels is examined. The critical face pressure estimates are very close to 3D numerical results, obtained by finite difference displacement method, and the optimized critical mechanism compares remarkably well with experimental and numerical observations.