This paper suggests that a simple micro-scale approach combined with a macro-scale approach to determine equivalent design parameters provides effective numerical modeling of pre-reinforced zones in a tunnel. This new technique enables the determination of the equivalent stiffness of pre-reinforced zones with a series or parallel combination of ground, grout bulb, and steel pipe stiffness. For verification, the authors compared the 3D numerical results from the suggested approach with the results of a precisely-simulated model which has the best precision. The comparison suggests that two cases achieve the best approximation to the solution: one case is related to the series-parallel stiffness system (SPSS) in which a bulb and steel are coupled in parallel and then connected to the ground in series; the other case is related to the series stiffness system (SSS) in which only a bulb and steel are coupled in series. The SPSS is recommended for calculating the stiffness of pre-reinforced zones because the SSS is inconvenient and time-consuming. The SPSS provides a slightly bigger vertical displacement at the crown of a tunnel in weathered rock than in other cases, and it produces almost identical results to a precisely-simulated model of horizontal displacement at the tunnel springline and at the ground surface settlement. The SPSS suggested in this paper effectively represents the behavior mechanism of pre-reinforced zones when compared to a precisely-simulated model.
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