Expectation of boulder frequency when tunneling in glacial till : a statistical approach based on transition probability

The aim of this study is the prediction of boulder frequency encountered during the construction of a tunnel in a morainic amphitheatre in northern Italy. This area is characterized by the presence of glacial and fluvioglacial deposits from the Pleistocene age. The ability to predict the size and frequency of boulders during construction is essential for assessing the type of machines to be used for tunneling and the related cost. Borehole data from site exploration programs do not provide sufficient information (e.g. frequency, size and location) on boulders embedded in the studied deposits. Statistics regarding boulder sizes, however, can be inferred from borehole data through the application of geostatistical techniques. A new estimation method is proposed that utilizes a transition probability-based geostatistical approach (TPROGS) to model spatial variability of boulders by 3-D Markov chains. T-PROGS has several advantages over traditional geostatistical methods because it has a conceptual framework for incorporating a considerable amount of geological information into the development of simulations. This is accomplished by linking fundamental observable geological attributes (e.g. mean lengths, material proportions, anisotropy, and lithofacies juxtaposition) with Markov chain model parameters. The geological database used consists of the following: borehole data, geological survey of the excavation, outcrop measurement of boulder characteristics and an interpretative geological cross-section across the study area. The result of geostatistical simulations allowed prediction of the size, frequency distribution and location of boulders during the construction of the tunnel. The higher value of boulder concentration corresponds to glacial deposits, where a concentration of 27 boulders/10,000 m³ of sediments has been simulated. Furthermore, the variability between different simulations that have been computed allowed quantification of the uncertainty.