Elastoplastic analysis of the tunnel considering the nonlinear variations of the strength parameters from peak to residual in the strain softening stage

The ground response curve, (GRC), is one of the three important components of convergence- confinement method. In fact, this curve is obtained from elastic-plastic analysis of circular tunnel, which is various depending on the type of rock around an excavation, mechanical, geometrical features of it. Tunnel geometry, in situ stress, support pressure, intact rock features and fractured rock mass features, are among the effective factors on the ground response curve. Elastic-plastic analysis of a circular opening subjected to hydrostatic far-field stress has been one of the most fundamental problems related behavior of tunnels. The results of such analysis can be shown in the ground response curve. In this curve, the ratio of radial convergence of tunnel to inner pressure of tunnel is presented by with distance from tunnel face scale. This analysis can be expressed in this way relation between the convergence of the tunnel wall and radius of plastic zone around the tunnel. In this paper is presented a relatively simple procedure for the ground response curve of the circular tunnels excavated in strain softening behaviors, compatible with a nonlinear Hook-Brown yield criterion. In order to construct true GRC, it is necessary to think about the selection of the behavior parameters of rock mass and its yield criterion and analyses different states. Material with elastic-plastic behavior according to behavior after fracture are divisible to three groups including perfect plastic, perfect brittle and strain-softening. Based on the reviewed the present studies, strain-softening model is closer to behavior reality of rock masses, but the convincing methods for recognition of rocks with strain-softening behavior, has not been presented up to now. The main reason of this deficiency is the complexity of analysis of rock mass with strain-softening behavior. Lack of closed form solution for determining the relation between convergence of tunnel and inner pressure, add sth. to this problem. Most researchers, for investigation of strain-softening behavior of materials, have considered the change of the strength parameters from peak to residual in the strain softening zone as a linear function. Therefore in this article, in order to more precisely investigate the strain softening behavior, these variations are nonlinearly modeled. Therefore, dilation and friction angle parameters and the constants of the yield criterion are variable from the peak to the residual. In order to show the applicability and accuracy of the proposed procedure and investigate the effect of it in plastic region, some illustrative examples are presented here. First, the effect of different definitions for the softening parameter η is discussed by means of elasto-plastic analysis of a circular tunnel using Park, 2007 data . Second, the effect of variation of critical softening parameters on the displacement of a circular tunnel is examined by the proposed method using Carranza-Torres, 2004 data. Then the effect of different definitions for strength parameters from peak to residual, in the softening zone is evaluated by constructing the ground response curves for Park, 2007 data.