ABSTRACT
A viscoplastic model with instantaneous failure is proposed and applied to the calculation of the closure of a circular gallery. A practical application of these calculations concerns the effects of initial critical construction phases of a tunnel on its ultimate equilibrium, when the rockmass exhibits delayed behavior. Special attention is paid on effect of loading rates ; a stability condition is shown off, when the internal pressure rate is prescribed.
INTRODUCTION
To analyse delayed phenomena occuring in deep galleries, different models for the mechanical behavior of the rockmass have been proposed in litterature, and a tentative of classification has been given (Nguyen Minh D., 1986). For instance, viscoplastic models, similar to the Bingham one and including strain-softening behavior to interprete delayed failure, give good agreement for long term response of lined excavation (Borsetto and al., 1978; Nguyen Minh D. and al., 1982 ; Rousset, 1985 ; ...). However, such models seem to be inadequate to study the influence of short term events (tunnelling and support placement phases) on the final stability of the work; they would suggest that the ultimate support pressure mainly depends on the closure rate at the moment when the con- tact between lining and rockmass is achieved. Such an analyse is not sufficient. Indeed, during the primary stages of the excavation, the surrounding rockmass is submitted to severe loadings and high strain rates, which, in some cases, can lead to uncontrollable failure near the wall. In practice, provisory lining using rockbolt wire netting, shotcrete or yieldable ring sets and arches, aim to take into account these phenomena. Therefore, in these cases, it is necessary to consider the short term strength of the material. For this purpose, a rheological model, including both viscoplasticity to represent delayed behavior and instantaneous plasticity with strain softening to describe short term failure, is proposed and applied to solve the problem of a deep circular gallery. Special attention is paid to the influence on the long term stability of the work, of loading rates which are linked to the construction phase parameters (tunnel face advance, delay before lining installation, etc...). The paper presented here is complementary to another one (D. Nguyen and G. Rousset, 1987).
1 RHEOLOGICAL MODEL
The rheological model is made of two different groups in series (fi-gure 1) : (mathematical equation)(available in full paper)
2 APPLICATION TO THE CLOSURE OF A CIRCULAR GALLERY
2.1 Geometry
Consider now the problem of a circular gallery (radius = 1), driven in an homogeneous and isotropic medium. Let P8 be the overburden pressure and Pi the internal pressure applied onto the wall of the gallery. The problem is treated, assuming plane strain condition. According to the well-known convergence-confinement concept, Pi(t) is initially equal to P8, and will vary as time passes, in a manner depending on construction phases (Panet et al., 1982; Fairhurst et al, 1980). In the general case, several zones appear on the wall and progress into the medium as the closure proceeds.
