RELIABILITY-BASED STUDY OF CIRCULAR TUNNELS IN ELASTIC MEDIA BY USING THE BOUNDARY ELEMENT METHOD

Resumo

Problems involving cavities or excavations are widely addressed in geomechanics, in both
analytical and numerical approaches. The Boundary Element Method (BEM) is well-known as an
interesting choice for the analysis of problems involving semi-infinite domains, providing accurate
results at a low computational cost. The study of circular tunnels is traditionally performed through a
deterministic approach, not considering the uncertainties inherent to the design variables. Since the
properties of geomaterials vary in a considerable range, the use of mean or characteristic values in the
deterministic methodology does not comprise the several combinations of critical random values (r.v.)
of the variables, for the different failure modes considered. This work deals with the probabilistic
analysis of circular tunnels embedded in elastic media, by coupling a BEM formulation to a structural
reliability model. Some of the loads applied and material parameters are treated as random variables,
whose statistical description is found in the literature. The loadings considered include the vertical
overburden stress and the lateral earth pressure. Regarding the reliability evaluation, First Order
Reliability Method (FORM) and Monte Carlo simulation technique are employed, being compared in
terms of accuracy. Regarding the BEM model, the Multiple Reciprocity Method (MRM) is used in the
evaluation of domain integrals, and the sub-region technique is employed for the analysis of the tunnel
lining. Some examples are presented, in order to validate the coupled BEM-FORM model and apply it
to the estimation of failure probability, evaluating the influence of the r.v. taken into account in the
probabilistic response.