Contents lists available at ScienceDirect Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust Efficient 3D probabilistic stability analysis of rock tunnels using a Lattice Model and cloud computing Leandro L. Rasmussen a, ⁎ , Pedro P. Cacciari b , Marcos M. Futai b , Márcio M. de Farias a , André P. de Assis a a Departamento de Engenharia Civil e Ambiental/FT – Universidade de Brasília, 70910-900 Brasília – DF, Brazil b Escola Politécnica – Universidade de São Paulo, Av. Prof. Luciano Gualberto, travessa 3 n° 380, 05508-010 – SP, Brazil ARTICLE INFO Keywords: Lattice Probabilistic Rock tunnel Cloud computing ABSTRACT In this paper, the Classic Lattice Spring Model is developed in order to be applied to probabilistic stability analyses of rock tunnels in low in situ stress environments, where the falling of blocks is the main failure mechanism. For this objective, the method is combined with the Synthetic Rock Mass technique and Barton- Bandis joint constitutive model, giving it a series of advantages: simulations with deformable blocks; possible formation of tension cracks; and an appropriate constitutive model for the mechanical behavior of joints. The use of cloud computing technology is proposed for efficient probabilistic analyses using the Monte Carlo simulation. A case study is presented based on an unsupported section of a shallow rock tunnel excavated in the state of Espírito Santo, Brazil. A 3D probabilistic stability analysis of the tunnel is performed with the proposed meth- odology. From the results, a positional probability map is elaborated, which indicates the likelihood of block failure around the excavation cross-section. The unstable zones indicated by the map are then compared to the failed region of the real tunnel so as to demonstrate the competence of the methodology. 1. Introduction Rock is one of the most complex material ever found in any en- gineering field (Fairhurst, 2013). The complexity of rocks and rock masses has been the cause of unexpected outcomes during the ex- cavation works of rock tunnels, involving both major financial losses as well as fatalities. Consequently, research has focused on the develop- ment of novel design methodologies capable of ensuring safer en- gineering projects. Due to the uncertainties involved in rock engineering design, probabilistic-based methods are preferred over deterministic ones (Johansson et al., 2016). The reason is that the former may consider the effects of uncertainties more stringently. This becomes specially re- levant in the case of underground excavations in rock due to the sto- chastic nature of the joint sets. Studies have been performed on the application of probabilistic approaches to deterministic failure models (Chen et al., 1997; Park and West, 2001; Low and Einstein, 2013). Nonetheless, their main dis- advantage resides on the choice of an appropriate failure mechanism. It has already been shown that, depending on the deterministic model selected, there can be a variation of up to two orders of magnitude on the probability result (Li and White, 1987). Furthermore, these methods usually neglect the conditional probability related to the existence of the failure mode under consideration. In order to overcome the problems aforementioned, the fracture of a rock mass should also be treated as a random variable. The develop- ment of the Discrete Fracture Network method (DFN) (Lei et al., 2017) and joint system models (Dershowitz and Einstein, 1988) paved the way to achieve this objective. On the other hand, these methods are no longer amenable to simple analytical solutions and computational methodologies become mandatory for their application. Thanks to the advancement of computing technology, new analysis tools are being developed which combine Discrete Fracture Networks and probabilistic methods. Based on the key-block theory and vectorial stability analysis of blocks proposed respectively by Goodman and Shi (1985) and Warburton (1981), computer programs have been devel- oped to make use of stochastic DFN generation for evaluating the probability of rock block failure within underground excavations (Jakubowski, 1995; Song et al., 2001; Merrien-Soukatchoff et al., 2012; Fu et al., 2016; Napa-García et al., 2017). The Key-Block theory and limit equilibrium approach are inter- esting for their swift calculation procedure. Nevertheless, their main https://doi.org/10.1016/j.tust.2018.12.022 Received 11 April 2018; Received in revised form 29 October 2018; Accepted 23 December 2018 ⁎ Corresponding author. E-mail address: leandro.lima.ra@gmail.com (L.L. Rasmussen). Tunnelling and Underground Space Technology 85 (2019) 282–293 0886-7798/ © 2018 Elsevier Ltd. All rights reserved. T