Rock-support interaction concepts, which are applied to support systems such as concrete linings and ungrouted rockbolts, cannot be applied to grouted rockbolts, because of the nature of the structural interaction of the rock mass and grouted rockbolts. In this paper, by assuming the grouted rockbolts increase internal pressure within a broken rock mass, and with consideration of a nonlinear strength criterion for rock mass and on the basis of brittle behavior model and rock-support interaction concepts, a new analytical approach for the computation of the ground response curve for a circular bolted tunnel (having been reinforced with active grouted rockbolts) under hydrostatic stress field is derived while the effect of distance of bolted section to tunnel face has been also considered. Because of algebraic complexity, it is not possible to obtain closed-form solutions; therefore a computer program was prepared for solving the problem on the basis of numerical methods.
In rock engineering, rockbolts have been used to stabilize openings for many years. The rock bolting system may improve the competence of disturbed rock masses by preventing joint movements, forcing the rock mass to support itself . According to the previously researches, the rock bolting effects are summarized as the ground sewing, adding pressure on the tunnel boundary , cohesion improving , better geomechanical properties (both cohesion and friction angle) of rock mass , overall variation of rock mass properties, . In order to simulate rock bolting effect and modeling of them as a support system in underground excavations different numerical, experimental, and analytical studies has been also cried out. Li and Stillborg  eloped three analytical models for rock bolts: one for bolts subjected to a concentrated pull load in a pullout test, another one for bolts installed in uniformly deformed rock masses, and the last one for bolts subjected to the opening of individual rock joints. The development of the models is based on the description of the mechanical coupling at the interface between the bolt and the grout medium for grouted rockbolts, or between the bolt and the rock for frictionally coupled bolts. Yue Cai et al.  proposed an analytical model to predict the axial force of grouted rock bolt in the tunnelling design. In this approach, the interaction mechanism of the rock bolt and the soft rock mass is described according to their consistent displacement and coupling and decoupling behaviors of the rockbolts around a circular tunnel is analyzed. By using this model, a way is supplied to analyze the supporting behavior of the rock bolt. Oreste  presented a new calculation procedure for the analysis and dimensioning of fully grouted radial bolts in tunnels. This procedure is based on the principle of congruency of the displacements, imposing the condition that the lengthening of the bolt is equal to the expansion in the radial direction of the reinforced rock annulus.