A new procedure for ground response curve (GRC) in strain-softening surrounding rock

Abstract

A new procedure for the ground response curve (GRC) is investigated in strain-softening surrounding rock for a circular opening. The procedure started each step with a radius increment and the analytical solutions of stress and strain in each annulus were presented. The plastic region is divided into a finite number of concentric annuli, whose thickness is uniformly determined by a small radius increment. Combining the equilibrium equation and failure criterion, stress for each annulus can be obtained analytically. The displacement for each step can be calculated analytically through solving the differential equation by invoking flow rule and Hooke’s law. The strains for each annulus can be obtained by the strain-displacement relationship. In the successive manner, the distributions of stress and displacement can be found. It should be noted that the finial stress and displacement at radial direction are the internal support pressure and deformation at the excavation surface, respectively. By assuming different plastic radii (using a plastic radius increment), GRC, the evolution curve of plastic radii and internal support pressure can be obtained analytically. Some numerical and engineering examples are performed to demonstrate the validity of the proposed procedure. It is shown that the results of the proposed procedure at the tunnel crown are basically consistent with field measuring data. The influence of the annulus number, plastic radius increment and dilation on the accuracy of the proposed approach is investigated. Results show that the solutions are more accurate and the calculation efficiency is higher.