The paper synthetically deals with the procedures frequently used to assess the opening convergence, to design the temporary lining, to evaluate the stress and displacement that are characteristics of the achieved equilibrium state. The stiffness of the lining, in its actual shape and not with the usual closed ring modeling, is evaluated; settling lining supports are taken into account as well as differentiated and evolving stresses in the bolts. The results obtained by an extensive parametric study allow the pointing out of some remarks and comparisons.


Viennent ici summarisees les plu usuel methodes pour I'evalutation des deplacements radiaux du fouille, pour Ie dimensionnement du revêtement provvisoire et pour la determination de la contrainte et du deplacement à l'quilibre, La rigidite du revêtement dans sa geometrie reelle est evaluee, Aussi bien les liasions, aussi avec des deplacements, que les differents contraintes des boulons d'ancrage, variables avec les deplacements radiaux, sont consideres. Les nombreuses analises effectuees permettent considerations et comparations.


Es werden, zusammenfassend, die ueblichen annaherungversuche erinnert, um die radialverschiebungen der baugrube zu schatzen, um die auskleidung zu bemessen, um den charakteristischen druck und verschiebung des erreichten gleichgewichts zu messen. Die steifheit der auskleidung wird in seiner echten form geschatzt und nicht als ob man sie als ring vorzutauschen wuerde; auch nachgiebige stuetze und unterschiedenen in den ankerschrauben werden geschatzt, Die nach ausgedehnten analysen erreichten ergebnissen, erlauben betrachtungen und vergleiche.


The study of the interaction between the tunnel opening having radius a and the lining is usually undertaken, excluding the cases when FEM or analogous methods are applied, resorting to the well known "characteristic curve" method (Lombardi 1973; Amberg & Lombardi 1974) or "convergence support" method (Gesta et al 1978). The opening starts deforming from an initial state characterized by the isotropic stress °; the lining, reacting, limits the convergence Δa = f(p) which takes place when the pressure p varies; the representation of this phenomenon is shown in Fig. 1. 1. In the cross-section, distant from the face, where it is allowable to consider plane-strain conditions, the characteristic curve of the cylindrical cavity (CCC)- Δa = f(p) can be defined. In this case the stress state and the radial deformation are known (Obert & Duvall 1967; Lembo Fazio & Ribacchi 1986); their expressions as well as the principle and the parameters which characterize the rock mass are reported in Berardi & Berardi (1996). In these expressions, when evaluating the zone in plastic state, the dilatancy has been taken into account as a factor varying with the stress state (Ladanyi 1974) rather than a chosen constant (0.5 2%), as is often considered in a simple manner (Amberg & Lombardi 1974). 1.2 The analysis of the behaviour of the tunnel face involves considerable difficulties; the 3D stress-strain state as well as the influence of the techniques and phases of construction play in fact a very important role. Moreover it is difficult to assess the value of the convergence (Δa)° that has already taken place in the section where the already placed lining part starts reacting. The relationship between the radial displacement (Δa)° and the pressure p is, in this case, defined as the characteristic curve of the face (CCF). Many approaches supply expressions for the CCF; the ones used in the following are briefly summarized.

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