In this paper, two new analytical approaches are presented on the basis of convergence-confinement method to compute both the ultimate convergence of circular tunnel and its plastic zone having been reinforced by systematically pre-tensioned fully grouted rockbolts. The models have two basic assumptions: (1) the grouted rockbolts increase the radial internal pressure within a broken rock mass by both the pre-tensioned force and the probable following induced force due to rock mass movement (2) tunnel convergence (specially short-term) occurs only due to reducing and diminishing of the radial constrained stress on tunnel surface provided by the working face. Hence, the values of both the pre-tensioned pressure and the mentioned radial constrained stress are specially taken into consideration in this paper. That is, according to their magnitudes, two different conditions occur: the magnitude of pre-tensioned pressure is greater than that of the constrained stress at bolt installation time and vice versa. The solutions are extended to each of conditions, and illustrative examples are solved. The proposed approaches predicting almost identical results show that pre-tensioning of grouted rockbolts will increase the efficiency and effectiveness of rockbolts.
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