Research Paper Time-dependent tunnel deformations in homogeneous and heterogeneous weak rock formations Atsushi Sainoki a,⇑ , Shingo Tabata b , Hani S. Mitri c , Daisuke Fukuda b , Jun-ichi Kodama b a International Research Organization for Advanced Science and Technology, Kumamoto University, Kumamoto City, Kumamoto Prefecture 860-8555, Japan b Division of Sustainable Resources Engineering, Hokkaido University, Sapporo City, Hokkaido 060-8628, Japan c Department of Mining and Materials Engineering, McGill University, Montreal, Quebec H3A 0E8, Canada article info Article history: Received 25 February 2017 Received in revised form 25 June 2017 Accepted 16 August 2017 Keywords: Time-dependent tunnel deformation Numerical analysis Weak rock formation Tertiary creep abstract To investigate long-term, time-dependent tunnel deformations, this study employs a non-linear rheolog- ical model capable of considering the tertiary creep behaviour of the rock mass (Okubo and Fukui, 2006). A model parametric study is undertaken with a 3D numerical model encompassing a tunnel. The results show that the tunnel walls start to deform at an accelerating rate after a lapse of ten years. The results offer an explanation to previously reported tunnel instability cases. A 3D numerical model encompassing weak rock formation obliquely intersecting with the tunnel is then constructed. The analysis yields asym- metric wall deformation pattern, suggesting the need for optimizing rock supports. Ó 2017 Published by Elsevier Ltd. 1. Introduction Despite recent advances in tunneling technologies, it is still a challenging task to ensure the stability of the tunnel over its planned service life. This is particularly true when a tunnel is dri- ven through weak rock formations. More attention needs to be paid to the behaviour of such weak rock mass to prevent instability from taking place. To date, a number of studies have been under- taken to better understand the effect of weak rock formations such as a fault zone on the stability of a tunnel [1–4]. Nilsen [2] con- ducted case studies to investigate cave-in and rock fall that occurred in tunnels constructed through weak rock mass in Nor- way. One of the case studies shows that rock fall took place in an area where a fault zone containing swelling clay intersects with the tunnel. Interestingly, there were no noticeable signs of instabil- ity during the construction of the tunnel. Based on the case studies, Nilsen (2011) concluded that the presence of swelling clay plays a key role in causing instability over time. It is also indicated that the time period required for the development of instability varies from several hours to more than 10 years. Huang et al. [5] performed experiments using a physical model that represents a tunnel inter- secting with a weak rock layer. The failure pattern observed from the test is then compared with those derived from numerical anal- ysis. Additionally, a model parametrical study was carried out while varying several parameters, such as dip angle of the weak interlayer and the distance between the tunnel and the interlayer. For the numerical analysis, a plastic damage model is used to model the weak interlayer, whereby deformation modulus is decreased with the evolution of plastic strain. Mao and Nilsen [3] performed elasto-plastic analyses to investigate the behaviour of a tunnel intersecting with a weakness zone. A model parametrical study with respect to the width of the weakness zone is conducted. Dong et al. [6] constructed a 3-D model to assess the impact of tun- nel excavation in geologically weak zones on surrounding con- structions, such as highway. Thus, it can be said that numerical approaches have been attempted assuming elasto-plastic behaviour of weak rock forma- tions to assess tunnel stability. It should be noted, however, that the time-dependent behaviour of the rock mass is also critical in predicting tunnel stability. Since the last century, significant efforts have been made to clarify the time-dependent behaviour of rock surrounding underground openings in civil and mining engineer- ing projects [7–22]. For instance, Nadimi et al. (2011) carried out laboratory tests to obtain parameters for a power constitutive creep model. Using the estimated parameters, they performed numerical analysis with 3-dimensional discrete element modelling while considering the time-dependent behaviour of the rock mass around a cavern. The results obtained from the numerical simula- tion coincide well with deformations monitored in the field. Stress hardening elastic viscous plastic model and three-stage creep model were employed in previous case studies [14,15] for a tunnel excavated through extremely weak formations to examine http://dx.doi.org/10.1016/j.compgeo.2017.08.008 0266-352X/Ó 2017 Published by Elsevier Ltd. ⇑ Corresponding author at: Kurokami South C4 Room 105, 2-39-1 Kurokami, Chuo-ku, Kumamoto City, Kumamoto Prefecture 860-8555, Japan. E-mail address: atsushi_sainoki@kumamoto-u.ac.jp (A. Sainoki). Computers and Geotechnics 92 (2017) 186–200 Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo