On account of the complexity of the problem, the use of a conventional method presented with numerous questions concerning the choice of the geometrical and mechanical characteristics to put into the analysis. The probabilistic approach appeared as the only possible one. It allows to take into account parameters with a considerable variation, as well as random actions like earthquakes. The computing technique uses the Rosenblueth's multivariate point estimate method. The probability of failure was computed before, during and after the works, as well as the anchor forces required to keep this probability below a reasonable level.
En raison de la complexite du problème, l'application d'une methode traditionnelle posait de nombreuses questions quant au choix des caracteristiques geometriques et mecaniques à introduire dans les calculs. Il est ainsi apparu que la seule approche possible etait l'approche probabiliste, qui permet de prendre en compte des paramètres presentant une variation appreciable, ainsi que des sollicitations ayant un caractere aleatoire comme les seismes. La technique utilisee est la methode d'estimation ponctuelle de Rosenblueth avec variables multiples. La probabilite de rupture a ete calculee avant, pendant et après les travaux, ainsi que les ancrages necessaires pour maintenir cette probabilite à un ni veau acceptable.
Die Anwendung einer traditionellen Methode musste in Frage gestellt werden, da sich durch die Komplexitat des Problems bei der Wahl der geometrischen und mechanischen Eingabedaten Schwierigkeiten ergaben. Eine probabilistische Methode erwies sich als die einzige Lösungsmöglichkeit. Sie erlaubt, sowohl Parameter, die betrachtlichen Schwankungenunterliegen, als auch seltene Beanspruchungen wie Erdbeben, zu beruecksichtigen. Zur Anwendung kam die multivariate punktapproximierung nach Rosenblueth. Die Versagenswahrscheinlichkeit wurde vor, wahrend und nach dem Bau berechnet. Zudem wurden diejenen Ankerkrafte ermittelt, bei denen diese Wahrscheinlichkeit ein vernuenftiges Niveau nicht ueberschreitet.
The building of the Northern mouth of the motorway tunnels, described by Delapierre et al. in the here above communication "Methodologie pour le calcul de la stabilite des tunnels autoroutiers", requires the opening of a large excavation at the toe of a slope. A 50 m wide and 20 m high piles wall will be bored and anchored in the hill. The weathered rock mass exhibits a rather complex geometry of fractures, faults and bedding planes, with a very large scatter in the mechanical properties. Furthermore, several slides occured in the vicinity during the last years and the actual seems to be rather unstable. The site is located in an active seismic area and a seismic action cannot be ignored.
The "block theory" (Goodman and Shi, Hoek and Bray) method was modified to include the effect of the piles wall and its anchors. The shear resistance of the wall has been taken in account, and the geometry of the moving volume was adapted to conform with the geometry of the wall and with the, increase of the strength with depth. The moving volume is therefore defined by the wall itself, the natural slope and any valid combination of the planes of discontinuity inside the rock mass. The acting forces are the weight, the seismic actions and water pressures along discontinuity planes. The resisting forces include cohesion and friction along the sliding planes, and several external actions (shear strength in the wall, anchors, Ko-pressures). The soil of the upper most layer have similar properties as the heavy weathered rock mass and is not considered separately.
A deterministic method requires the choice of "probable" or "likely" values for each parameter involved in the computing method, and the result is expressed as a "safety factor" which has to be compared with allowable values. In this particular case, this choice of the parameters, particulary the geometry and the mechanical strength of the discontinuity planes, is almost impossible due to the very large scatter of the observed values. The probabilistic method allows the use of parameters given by their probability distributions, and the results of such a method are also probability distributions. A failure is defined as, for instance, the occurence of negative values for the safety margin (difference between acting and resisting forces), and the "probability of failure" is defined as the probability of such an occurence. Numerous applications were carried out in the past using the classical methods: the Taylor-series expansion, the Monte-Carlo simulation. Both methods have limitations, particularly when the algorithm becomes complex and with correlated random variables.
