ACTA GEOTECHNICA SLOVENICA, 2012/2 37. about the authors Mohammad Reza Zareifard Amirkabir University of Technology Tehran, Iran E-mail: zareefard@aut.ac.ir corresponding author Ahmad Fahimifar Amirkabir University of Technology Tehran, Iran E-mail: fahim@aut.ac.ir Abstract A new, elasto-plastic, analytical-numerical solution, considering the axial-symmetry condition, for a circular tunnel excavated in a strain-sofening and Hoek–Brown rock mass is proposed. To examine the efect of initial stress variations, and also the boundary conditions at the ground surface, the formulations are derived for diferent directions around the tunnel. Furthermore, the efect of the weight of the plastic zone is taken into account in this regard. As the derived diferential equations have no explicit analytical solutions for the plastic zone, the fnite-diference method (FDM) is used in this study. On the other hand, analytical expressions are derived for the elastic zone. Several illustrative examples are given to demonstrate the performance of the proposed solution, and to examine the efect of various boundary conditions. It is concluded that the classic solutions, based on the hydrostatic far-feld stress, and neglecting the efect of the boundary conditions at the ground surface, give applicable results for a wide range of practical problems. However, ignoring the weight of the plastic zone in the analyses can lead to large errors in the calculations. Keywords ground-response curve, elasto-plastic analysis, boundary condition, axial symmetry, gravitational loads 1 INTRODUCTION A number of methods are currently used for the design and analysis of tunnels. Among them, the convergence- confnement method (the C.-C. method) has played an important role in providing an insight into the interac- tion between the lining support and the surrounding ground mass. Te C.-C. method is based on a concept that involves an analysis of the ground-structure interaction by independent studies of the behavior of the ground and of the tunnel support. In this regard, the ground behavior is represented by a ground-response curve; which describes the ground convergence in terms of the applied internal pressure. However, to maintain simplicity, a number of simplifying assumptions are made in its derivation. Tese assumptions make the method applicable only to deep tunnels in hydrostatic stress felds. In the past, a number of classic solutions for determining the ground-response curve have been published. Tese solutions may be categorized into two groups of analytical closed-form solutions and analytical-numerical unclosed-form solutions. Although a number of closed-form solutions are available (such as that proposed by Brown et al. [1]; Sharan [2]; Carranza- Torres [3]; Park and Kim [4]), each solution sufers from a level of approximation in the sense that it incorporates various simplifying assumptions. For example, these solutions have been proposed for the rock masses with simpler behavior models, including the elastic-perfect- plastic or elastic-brittle-plastic behavior models. In fact, for more complicated behavior models obtaining an exact closed-form solution is impossible. On the other hand, in the unclosed-form solutions (Brown et al., [1]; Guan et al., [5]; Lee and Pietruszczak, [6]; Fahimifar and Zareifard, [7]), consideration of more complicated and general material-behavior models are possible. However, all the mentioned solutions (both the closed- and unclosed-form solutions) are based on the classic assumptions made in the C.-C. method. Diferent aspects of the C.-C. method have been investigated by researchers, both analytically and numerically. A NEW SOLUTION FOR SHALLOW AND DEEP TUNNELS BY CONSIDERING THE GRAVITATIONAL LOADS MOHAMMAD REZA ZAREIFARD and AHMAD FAHIMIFAR