Some parametric studies about the influence of discontinuity properties on tunnel behaviour are reported, considering overstressed joints. Stress and displacement fields are presented, and a comparison is made with isotropic and anisotropic, analytical or numerical continuous solutions.


On presente des etudes par elements finits sur I'influence des proprietes des discontinuites dans le comportement des tunnels en roche où la resistance au cisaillement des discontinuites est depassee. Une comparaison est faite avec des solutions numeriques et analytiques pour massif continu, soit isotropique soit anisotropique.


Es wi rd von einigen parametrischen FE - Untersuchungen ueber den Einfluβ der Diskontinuitatseigen schaften auf das Verhalten von Tunnels im Felsen berichtet, wobei die Wirkung der Spannungen beruckslchtigt - wird. Spannungs - und Verschiebungsfelder werden vorgestellt, und ein Vergleich mit isotropen und anisotropen, analytischen oder numerischen Kontinuumlösungen gezogen.


The random pattern of the discontinuities, the scattering of their geometric and mechanical characteristics and the heterogeneity and anisotropy of the rock assign to the rock masses a complex structural behaviour, the analysis and forecasting of which has to be done, due to computational and geotechnical data limitations, by means of continuous or discontinuous simplified models. The verisimilitude and meaning of such approaches are directly dependent on the macroscopic structure of the rock masses, the discontinuous models requiring the definition of the mechanical properties both of the geomechanically important discontinuities and of the equivalent continuous medium between those joints. For shallow underground openings, with low stress levels, the deformation of the rock blocks can often be negligeable, if compared with the rotation and translation movements which take place along the joints, block models being then commendable for the stability analysis (Lamas, 1986). For deep tunnels in high stress fields, however, both block and joint deformation must be taken into account. Herein, the finite element method is a suitable tool, both in the investigation of the tunnel" phenomenology and in design. In the paper some parametric studies on the influence of discontinuity properties and primary state of stress on tunnel behaviour are reported. A comparison is made with isotropic and anisotropic, analytical or numerical continuous solutions. As overstresses induce joint failure, their effects are evaluated in terms of stress and displacement fields and the safety factors against sliding, along the discontinuities, are investigated.


A plane strain analysis of a circular tunnel (R=3 m) in a sedimentary rock mass with a main joint set was carried out. The geometrical and mechanical conditions of nine parametrical studies are described in figs. 1 and 2, considering the rock mass between discontinuities as a continuous elastic medium and assigning both linear and non-linear behaviour to joints. The initial vertical stress was v=2 MPa. Displacements, principal stresses and equal stress lines for all calculations were plotted and can be seen elsewhere (Cunha, 1981). As the existence of the main joint set gives the rock mass a clear anisotropic behavior, the definition of equivalent continuous elastic anisotropic media, based on the mechanical properties of the joints and rock matrix, was made for the several calculation. The displacement and stress fields relative to these equivalent media, when compared with the elastic discontinuous ones, show good similarities as regards the trend of stresses and displacements (Cunha, 1981). Fig. 3 describes the joint yielding lengths for the various calculations, yielding depending on joint position related to tunnel wall and only attaining joints II to VI. It can be observed that the extension of joint yielding is related to the decrease of joint stiffness or rock properties and to the direction of the maximum initial principal stress. Joint displacements and yielding extension are greater when this stress is parallel to the joint set. Yielding extension also increases when joint strength decreases or joint stiffness increases. When joint stiffness is equivalent to the deformability of the rock matrix, joint slidings were nil (J7), although joint strength, computed by the Mohr-Coulomb criterion, was exceeded for some joints. The yielding extension increases from invert to crown, where the maximum stress σθ is parallel to the joint set, thus developing a tangential effort on the joints. So the maximum yielding length occurs in joints III and IV, respectively located below and above the tunnel crown, and the same applies for joint displacement. In fig. 4 displacements and stresses of joints III and IV for all calculations are shown. The most unfavorable situation occurs when the maximum principal component, parallel to the joints (calculations J5, J8) brings about a slower vanishing of tangential stresses along the joints and an overall decrease in their safety coefficient against sliding, leading to an increase in the extent of the zones where the joint strength may be exceeded and, consequently, to an increase of joint slidings.

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