A comprehensive solution for the calculation of ground reaction curve in the crown and sidewalls of circular tunnels in the elastic-plastic-EDZ rock mass considering strain softening

Although the determination of ground reaction curve (GRC) for tunnels has been extensively studied, formation of a damaged zone around the tunnel along with effects of some new features, including intermediate principle stress, exponential decaying dilation parameter, weight of the damaged rock and Young's modulus variation in the excavation damaged zone (EDZ) on the GRC development have not yet been considered. In this paper, considering all the affecting parameters including the previously studied ones and the new features, a comprehensive solution for the calculation of GRC of circular tunnels is presented. First, defining a more realistic medium for medium quality rock mass, behavior of tunnel's surrounding rock mass is categorized into elastic, plastic and excavation damaged zones, where materials in the plastic zone experience a strain softening. Also, rock mass through this strain softening, elastic-plastic-EDZ medium obeys Unified strength criterion (USC). Next, regarding the new defined medium, radial stress at the plastic-EDZ boundary is numerically calculated. Defining separate normalized radiuses for the plastic and damaged zones, thickness of annuluses, also, stress and strain increments are derived for different regions through finite difference solution of governing equilibrium and compatibility equations. The results of the proposed algorithm are verified using the field measurement data of Hanlingjie tunnel, China and its high accuracy is shown. Also, omitting the new features of the proposed algorithm, its comprehensiveness is discussed through comparison with some available solutions in the literature and a very good consistency is obtained. On the other hand, considering new features of the proposed algorithm, a considerable discrepancy is achieved indicating the importance of consideration of these features in the ground reaction curve development.